# RD SHARMA Solutions for Class 10 Maths Chapter 14 - Surface Areas and Volumes

If you have a rectangular block or a sphere with specific dimensions, would you know how to make small spheres of a specific radius or diameter using the solid shape? To find answers to these kinds of questions, refer to TopperLearning’s NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes.

Understand the methods to find the surface area and volume of real objects such as toys, rockets etc. with our NCERT textbook solutions for CBSE Class 10 Mathematics. For further revision, go through our exam assistance resources such as sample papers, online practice tests etc.

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## Chapter 14 - Surface Areas and Volumes Exercise Ex. 14.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

2.2 cubic dm of brass is to be drawn into a cylindrical wire 0.25 cm in diameter. Find the length of the wire.

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Find the number of metallic circular discs with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

Solution 9

Question 10

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm × 42 cm × 21 cm.

Solution 10

Question 11

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.

Solution 11

Question 12

Three cubes of a metal whose edges are in the ratio 3 : 4: 5 are melted and converted into a single cube whose diagonal is  cm. Find the number of cones so formed.

Solution 12

Question 13

A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.

Solution 13

Question 14

Solution 14

Question 15

An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.

Solution 15

Question 16

Solution 16

Question 17

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Solution 17

Question 18

Solution 18

Question 19

How many coins 1.75 cm in diameter and 2 mm thick must be melted to form a cuboid 11 cm 10 cm 7 cm?

Solution 19

Question 20

Solution 20

Question 21

A cylindrical bucket, 32 cm high and with a radius of base 18 cm, is filled with sand. This bucket is emptied out on the ground and a conical heap of sand is formed. If the height of conical heap is 24 cm, find the radius and slant height of the heap.

Solution 21

Question 22

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cones formed.

Solution 22

Question 23

A solid cuboid of iron with dimensions 53 cm x 40 cm x 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Rain water, which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if a rainfall of 1 cm has fallen? [Use = 22/7]

Solution 35

Question 36

The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. if the rain water collected from the roof just fills the cylindrical vessel, then find the rain fall in cm.

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

150 spherical marbles, each of diameter 1.4 cm are dropped in cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel

Solution 46

*Answer given in the book is incorrect.

Question 47

Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which

of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by shushant ?

Solution 47

Question 48

16 glass spheres each of radius 2 cm are picked into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.

Solution 48

Question 49

Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

Solution 49

Question 50

Water in a canal 1.5 m wide and 6 m deep is flowing with a speed of 10 km/hr. How much area will it irrigate in 30 minutes if 8 cm of standing water is desired?

Solution 50

Question 51

A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Solution 51

Question 52

A cylindrical tank full of water is emptied by a pipe at the rate of 225 liters per minute. How much time will it take to empty half the tank, if the diameter of its base is 3 m and its height is 3.5 m? (π = 22/7)

Solution 52

Question 53

Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of the base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.

Solution 53

Question 54

Water flows at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will level of water in the pond rise by 21 cm?

Solution 54

Question 55

A canal 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?

Solution 55

Question 56

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, find the volume of cylinder.

Solution 56

Question 57

Solution 57

Question 58

Solution 58

Question 59

Solution 59

Question 60

A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. find the cost of cloth used at the rate of Rs. 25 per metre. (π = 22/7)

Solution 60

Question 61

Solution 61

Question 62

The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm2. If the volume of metal used in making the cylinder is 176 cm3, find the outer and inner diameters of the cylinder. (Use = 22/7)

Solution 62

Question 63

Solution 63

Question 64

Solution 64

Question 65

If the total surface area of a solid hemisphere is 462 cm2, find its volume.

(π = 22/7)

Solution 65

*Answer given in the book is incorrect.

Question 66

Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Solution 66

Question 67

A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylindrical full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Solution 67

Question 68

A heap of rice in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of rice. How much canvas cloth is required to cover the heap?

Solution 68

Question 69

A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Solution 69

Question 70

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

Solution 70

Question 71

A factory manufactures 120,000 pencils daily The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at Rs. 0.05 per dm2.

Solution 71

Question 72

πThe  part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

Solution 72

Height of the conical vessel h = 24 cm

Radius of the conical vessel r =5 cm

Let h be the height of the cylindrical vessel which is filled by water of the conical vessel.

Radius of the cylindrical vessel =10 cm

Volume of the cylindrical vessel = volume of water

π(10)2h=150π

h = 150π¸ 100π

h = 1.5 cm

Thus, the height of the cylindrical vessel is 1.5 cm.

## Chapter 14 - Surface Areas and Volumes Exercise Ex. 14.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemi-sphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub. (Take = 22/7)

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

A cylinderical road roller made of iron is 1 m long. Its internal diameter is 54 cm and the thickness of the iron sheet used in making the roller is 9 cm. Find the mass of the roller, if 1 cm3 of iron has 7.8 gm mass. (Use = 3.14)

Solution 16

Question 17

A vessel in the form of a hollow hemisphere mounted by a hollow cylinder. The dijameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

A right circular cylinder having diameter 12 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

A wooden toy is made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy.

(π = 22/7)

Solution 28

Question 29

The largest possible sphere is carved out of a wooden solid cube of side 7 cm. find the volume of wood left.(Use = 22/7)

Solution 29

Question 30

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. (π = 22/7)

Solution 30

Question 31

The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.

Solution 31

Question 32

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166. Find the height of the toy. Also, find the cost of painting the 6 hemispherical part of the toy at the rate of Rs. 10 per cm2. (Take π = 22/7).

Solution 32

Question 33

In Fig. 16.57, from a cuboidal solid metalic block, of dimensions 15 cm × 10 cm × 5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block. (Take π = 22/7).

Solution 33

Question 34

A building is in the form of a cylinder surmounted by a hemi-spherical vaulted done and contains  of air. If the internal diameter of done is equal to its total height above the floor, find the height of the building?

Solution 34

Question 35

A pen stand made of wood is in the shape of a cuboid four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm × 5 cm × 4 cm. The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

Solution 35

Question 36

A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to  of the total height of the building. Find the height of the building, if it contains  of air.

Solution 36

Question 37

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of cone is 4 cm and the diameter of the base is 8 cm. Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface area of the toy.

Solution 37

Question 38

A circus tent is in the shape of a cylinder surmounted by a conical top of same diameter. If their common diameter is 56m, the height of the cylindrical part is 6 m and the total height of the tent above the ground is 27 m, find the area of the canvas used in making the tent.

Solution 38

Total area of the canvas = curved surface area of the cone + curved surface area of a cylinder radius = 28 m height (cylinder) = 6 m

height (cone) = 21 m

l = slant height of cone

curved surface area of the cone = πrl

×28×35

=×28×35 = 3080 m2

curved surface area of the cylinder = 2πrh

=2××28×6

=1056

Total area of the canvas = 3080+1056 =4136 m2

## Chapter 14 - Surface Areas and Volumes Exercise Ex. 14.3

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

A milk container of height 16 cm is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs.44 per litre which the container can hold.

Solution 10

Question 11

A bucket is in the form of a frustum of a cone of height 30 cm with radii of its lower and upper ends as 10 cm and 20 cm respectively. Find the capacity and surface area of the bucket. Also, find the cost of milk which can completely fill the container, at the rate of Rs.25 per litre.

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

A solid cone of base radius 10 cm is cut into two parts through the mid-points of its height, by a plane parallel to its base. Find the ratio in the volumes of two parts of the cone.

Solution 18

Question 19

A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs. 10 per 100 cm2. (π = 22/7)

Solution 19

Question 20

In Fig. 14.75, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid.

).

Solution 20

Question 23

Solution 23

Question 21

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of two parts.

Solution 21

Let the height of the cone be H and the radius be R. This cone is divided into two equal parts.

AQ=1/2 AP

Also,

QP||PC

ThereforeAQD~ΔAPC.

So,

Question 22

A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many liters of milk it contains if it is full to the brim? If the milk is sold at 40 per litre, find the amount received by the person.

Solution 22

A bucket, made of metal sheet, is in the form of a cone.

R = 15 cm, r = 6 cm and H=35 cm

Now, using the similarity concept, we can writ

Volume of the frustum is

The rate of milk is Rs. 40 per litre.

So, the cost of 51.48 litres is Rs. 2059.20.

## Chapter 14 - Surface Areas and Volumes Exercise Rev. 14

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surfaces are in the ratio 8:5, determine the ratio of the radius of the base to the height of the either of them.

Solution 33

Question 34

[Use  = 22/7]
Solution 34

Question 35

Solution 35

Question 36

A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared Determine the diameter of the sheet.

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47

Solution 47

Question 48

Solution 48

Question 49

Solution 49

Question 50

Solution 50

Question 51

An iron pole consisting of a cylindrical portion 110 cm high and of base diameter 12 cm is surmounted by a cone 9 cm high. Find the mass of the pole, given that 1 cm3 or iron has 8 gram mass approximately. (Use = 355/115)

Solution 51

Question 52

Solution 52

Question 53

Solution 53

Question 54

Solution 54

Question 55

Solution 55

Question 56

Solution 56

Question 57

Solution 57

Question 58

Solution 58

Question 59

Solution 59

Question 60

Solution 60

Question 61

[Use  = 22/7]
Solution 61

Question 62

Solution 62

Question 63

Solution 63

Question 64

Solution 64

Question 65

Solution 65

Question 66

Solution 66

Question 67

A container open at the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill in the container at the rate of Rs. 21 per litre. (π = 22/7)

Solution 67

Question 68

A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the cone and of the remaining solid left out after the cone carved out.

Solution 68

Question 69

A cone of radius 4 cm is divided into two parts by drawing a plane through the midpoint of its axis and parallel to its base. Compare the volumes of two parts.

Solution 69

Question 70

A wall 24 m, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm × 16 cm × 10 cm. If the mortar occupies  of the volume of the wall, then find the number of bricks used in constructing the wall.

Solution 70

Question 71

A bucket is in the form of a frustum of a cone and holds 28.490 litres of water. The radii of the top and bottom are 28 cm and 21 cm respectively. Find the height of the bucket.

Solution 71

Question 72

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

Solution 72

Question 73

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape formed.

Solution 73

Question 74

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Solution 74

Question 75

Two solids cones A and B are placed in a cylindrical tube as shown in figure. The ratio of their capacities are 2 : 1. Find the heights and capacities of the cones. Also, find the volume of the remaining portion of the cylinder.

Solution 75

Question 76

An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice cream, provided that its 1/6 part is left unfilled with ice cream.

Solution 76

## Chapter 14 - Surface Areas and Volumes Exercise 14.88

Question 1

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is

(a) 12 m

(b) 18 m

(c) 36 m

(d) 66 m

Solution 1

After melting a sphere and converting it into a wire, the volume remains same.

So the correct option is (c).

Question 2

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is

(a) 63

(b) 126

(c) 21

(d) 130

Solution 2

So, the correct option is (b).

Question 3

A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is

(a) 1:3

(b)

(c) 1:1

(d)

Solution 3

So the correct option is (b).

Question 4

A solid sphere of radius r is melted and cast into the shape of solid cone of height r, the radius of the base of the cone is

(a) 2r

(b) 3r

(c) r

(d) 4r

Solution 4

Question 5

The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm, then height of the cone is

(a) 10 cm
(b) 15 cm
(c) 18 cm
(d) 24 cm

Solution 5

So, the correct option is (b).

Question 6

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 in and its slant height is 40 m, the total area of the canvas required in m2 is

(a) 1760
(b) 2640
(c) 3960
(d) 7920

Solution 6

So, the correct option is (d).

Question 7

The number of solid spheres, each of diameter 6 cm that could be molded to form a solid metal cylinder of height 45 cm and diameter 4 cm, is

(a) 3

(b) 4

(c) 5

(d) 6

Solution 7

So, the correct option is (c).

Question 8

A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then surface of the water rises by

(a) 4.5 cm
(b) 3 cm
(c) 4 cm
(d) 2 cm

Solution 8

So, the correct option is (a).

Question 9

If the radii of the circular ends of a bucket of height 40 cm are of lengths 35 cm and 14 cm, then the volume of the bucket in cubic centimeters, is

(a) 60060

(b) 80080

(c) 70040

(d) 80160

Solution 9

So, correct option is (b).

Question 10

If a cone is cut into two parts by a horizontal plane passing through the mid- point of its axis, the ratio of the volumes of the upper part and the cone is

(a) 1:2
(b) 1:4
(c) 1:6
(d) 1:8

Solution 10

So, the correct option (d).

Question 11

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be  of the volume of the given cone, then the height above the base at which the section has been made, is

(a) 10 cm
(b) 15 cm
(c) 20 cm
(d) 25 cm

Solution 11

So, the correct option is (c).

Question 12

A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is

Solution 12

So, the correct option is (b).

## Chapter 14 - Surface Areas and Volumes Exercise 14.89

Question 13

A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4 m across at the bottom. If it is 6 m deep, then its capacity is

(a) 176 m3

(b) 196 m3

(c) 200 m3

(d) 110 m3

Solution 13

So, the correct option is (a).

Question 14

Water flows at the rate of 10 meter per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

(a) 48 minutes 15 sec

(b) 51 minutes 12 sec

(c) 52 minutes 1 sec

(d) 55 minutes

Solution 14

So, the correct option is (b).

Question 15

A cylindrical vessel 32 cm high and 18 cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, the radius of its base is

(a) 12 cm

(b) 24 cm

(c) 36 am

(d) 48 cm

Solution 15

So, the correct option is (c).

Question 16

The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

Solution 16

So, the correct option is (d).

Question 17

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is

Solution 17

So, the correct option is (a).

Question 18

The curved surface area of a cylinder is 264 m2 and its volume is 924 m3. The ratio of its diameter to its height is

(a) 3:7

(b) 7:3

(c) 6:7

(d) 7:6

Solution 18

So, the correct option is (b).

Question 19

A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 8 cm

Solution 19

So, the correct option is (d).

Question 20

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

(a) 1 : 2

(b) 2 : 3

(c) 9 : 16

(d) 16 : 9

Solution 20

So, the correct option is (d).

Question 21

If three metallic sphere of radius 6 cm, 8 cm, 10 cm are melted to form a single sphere, the diameter of the sphere is

(a) 12 cm

(b) 24 cm

(c) 30 cm

(d) 36 cm

Solution 21

Volume of the sphere = Sum of the volume of the three spheres

So, correct option is (b).

Question 22

The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is

(a) 3 cm

(b) 4 cm

(c) 6 cm

(d) 12 cm

Solution 22

So, correct option is (c).

Question 23

The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

Solution 23

So, correct option is (a).

Question 24

A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

Solution 24

So, the correct option is (c).

## Chapter 14 - Surface Areas and Volumes Exercise 14.90

Question 25

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is

Solution 25

So, correct option is (d).

Question 26

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 6 an

Solution 26

So, the correct option is (b).

Question 27

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is

(a) 12 cm

(b) 14 cm

(c) 15 cm

(d) 18 cm

Solution 27

So, the correct option is (b).

Question 28

A solid piece of iron of dimensions 49 x 33 x 24 cm is moulded into a sphere. The radius of the sphere is

(a) 21 cm

(b) 28 cm

(c) 35 cm

(d) None of these

Solution 28

So, the correct option is (a).

Question 29

The ratio of lateral surface area to the total surface area of a cylinder with base diameter 1.6 m and height 20 cm is

(a) 1 : 7

(b) 1 :5

(c) 7 : 1

(d) 5 : 1

Solution 29

Diameter = 1.6 m = 160 cm

So, the correct option is (b).

Question 30

A solid consists of a circular cylinder surmounted by a right circular cone. The height of the cone is h. If the total height of the solid is 3 times the volume of the cone, then the height of the cylinder is

Solution 30

So, the correct option is (d).

Question 31

The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is

Solution 31

So, correct option is (b).

Question 32

The radii of two cylinders are in the ratio 3 : 5. If their heights are in the ratio 2 : 3, then the ratio of their curved surface areas is

(a) 2 : 5

(b) 5 : 2

(c) 2 : 3

(d) 3 : 5

Solution 32

So, the correct option is (a).

Question 33

A right circular cylinder of radius r and height h = 2r just encloses a sphere of diameter

(a) h

(b) r

(c) 2r

(d) 2h

Solution 33

The cylinder completely encloses the sphere.

Hence, diameter of the sphere = diameter of the cylinder = 2r

Now, h is also given to be 2r.

So, the correct option is (a) or (c).

Note: Both can be the answer since h = 2r.

Question 34

The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is

(a) 6 cm

(b) 8 cm

(c) 4 cm

(d) 7 cm

Solution 34

So, the correct option is (a).

Question 35

The height and radius of the cone of which the frustum is a part are h1 and r3 respectively. If h2 and r2 are the heights and radius of the smaller base of the frustum respectively and h2 : h1 = 1: 2 then r2 : r1 is equal to

(a) 1 : 3

(b) 1 : 2

(c) 2 : 1

(d) 3 : 1

Solution 35

So, the correct option is (b).

Question 36

The diameters of the ends of a frustum of a cone are 32 cm and 20 cm. If its slant height is 10 cm, then its lateral surface area is

Solution 36

So, the correct option is (c).

Question 37

A solid frustum is of height 8 cm. If the radii of its lower and upper ends are 3 an and 9 cm respectively, then its slant height is

(a) 15 an

(b) 12 an

(c) 10 cm

(d) 17 cm

Solution 37

So, the correct option is (c).

## Chapter 14 - Surface Areas and Volumes Exercise 14.91

Question 38

The radii of the ends of a bucket 16 cm high are 20 cm and 8 cm. The curved surface area of the bucket is

(a) 1760 cm2

(b) 2240 cm2

(c) 880 cm2

(d) 3120 cm2

Solution 38

So, the correct option is (a).

Question 39

The diameters of the top and the bottom portions of a bucket are 42 cm and 28 cm respectively. If the height of the bucket is 24 cm, then the cost of painting its outer surface at the rate of 50 paice/cm2 is

(a) Rs. 1582.50

(b) Rs. 1724.50

(c) RS. 1683

(d) Rs. 1642

Solution 39

So, the correct option is (c)

Question 40

If four times the sum of the areas of two circular faces of a cylinder of height 8 cm is equal to twice the curve surface area, then diameter of the cylinder is

(a) 4 cm

(b) 8 cm

(c) 2 crn

(d) 6 cm

Solution 40

So, the correct option is (b).

Question 41

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a) 1 : 2
(b) 2 :1
(c) 1 : 4
(d) 4 : I

Solution 41

So, the correct option is (c).

Question 42

A metallic solid cone is melted to form a solid cylinder of equal radius. If the height of the cylinder is 6 cm, then the height of the cone was

(a) 10 cm

(b) 12 cm

(c) 18 cm

(d) 24 cm

Solution 42

So, the correct option is (c).

Question 43

A rectangular sheet of paper 40 cm x 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is

(a) 3.5

(b) 7

(c) 80/7

(d) 5

Solution 43

So, the correct option is (a).

Question 44

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is

(a) 3

(b) 5

(c) 4

(d) 6

Solution 44

So, the correct option is (b).

Question 45

Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

a. 3 : 4

b. 4 : 3

c. 9 : 16

d. 16 : 9

Solution 45

Question 46

A right circular cylinder of radius r and height h (h > 2r) just encloses a sphere of diameter

a. r

b. 2r

c. h

d. 2h

Solution 46

Correct option: (b)

From the figure, it is clear that diameter of sphere is 2r.

Question 47

In a right circular cone, the cross-section made by a plane parallel to the base is a

a. circle

b. frustum of a cone

c. sphere

d. hemisphere

Solution 47

Correct option: (a)

In a right circular cone, the cross-section made by a plane parallel to the base is a circle.

Question 48

If two solid-hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is

a. 4πr2

b. 6πr2

c. 3πr2

d. 8πr2

Solution 48

Correct option: (a)

When two solid-hemispheres of same base radius r are joined together along their bases, it forms a sphere.

And, CSA of sphere = 4πr2

Question 49

The diameters of two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is

a. 32.7 litres

b. 33.7 litres

c. 34.7 litres

d. 31.7 litres

Solution 49

Question 50

A spherical ball of radius r is melted to make 8 new identical balls each of radius r1. Then r : r1 =

a. 2 : 1

b. 1 : 2

c. 4 : 1

d. 1 : 4

Solution 50