# Chapter 14 : Surface Areas and Volumes - Rd Sharma Solutions for Class 10 Maths CBSE

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

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.

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.

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.

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

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.

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.

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.

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.

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?

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.

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.

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.

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.

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]

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.

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

*Answer given in the book is incorrect.

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 ?

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.

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?

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?

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?

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)

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.

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?

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?

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 cm^{2}, find the volume of cylinder.

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)

The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm^{2}. If the volume of metal used in making the cylinder is 176 cm^{3}, find the outer and inner diameters of the cylinder. (Use = 22/7)

If the total surface area of a solid hemisphere is 462 cm^{2}, find its volume.

(π = 22/7)

*Answer given in the book is incorrect.

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?

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.

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?

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.

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?

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 dm^{2}.

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.

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)^{2}h=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

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)

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 cm^{3} of iron has 7.8 gm mass. (Use = 3.14)

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.

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.

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)

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)

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)

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

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 cm^{2}. (Take π = 22/7).

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).

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?

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.

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.

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.

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.

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

=π×28×35

=×28×35 = 3080 m^{2}

curved surface area of the cylinder = 2πrh

=2××28×6

=1056

Total area of the canvas = 3080+1056 =4136 m^{2}

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

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.

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.

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.

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 cm^{2}. (π = 22/7)

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.

).

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.

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

Therefore,ΔAQD~ΔAPC.

So,

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.

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

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.

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.

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 cm^{3} or iron has 8 gram mass approximately. (Use = 355/115)

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)

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.

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.

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.

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.

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.

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.

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.

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.

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.

## Chapter 14 - Surface Areas and Volumes Exercise 14.88

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

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

So the correct option is (c).

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

So, the correct option is (b).

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)

So the correct option is (b).

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

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

So, the correct option is (b).

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 m^{2} is

(a) 1760

(b) 2640

(c) 3960

(d) 7920

So, the correct option is (d).

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

So, the correct option is (c).

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

So, the correct option is (a).

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

So, correct option is (b).

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

So, the correct option (d).

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

So, the correct option is (c).

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

So, the correct option is (b).

## Chapter 14 - Surface Areas and Volumes Exercise 14.89

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 m^{3 }

(b) 196 m^{3 }

(c) 200 m^{3 }

(d) 110 m^{3}

So, the correct option is (a).

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

So, the correct option is (b).

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

So, the correct option is (c).

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

So, the correct option is (d).

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

So, the correct option is (a).

The curved surface area of a cylinder is 264 m^{2} and its volume is 924 m^{3}. The ratio of its diameter to its height is

(a) 3:7

(b) 7:3

(c) 6:7

(d) 7:6

So, the correct option is (b).

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

So, the correct option is (d).

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

So, the correct option is (d).

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

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

So, correct option is (b).

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

So, correct option is (c).

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

So, correct option is (a).

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

So, the correct option is (c).

## Chapter 14 - Surface Areas and Volumes Exercise 14.90

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

So, correct option is (d).

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

So, the correct option is (b).

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

So, the correct option is (b).

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

So, the correct option is (a).

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

Diameter = 1.6 m = 160 cm

So, radius = 80 cm

So, the correct option is (b).

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

So, the correct option is (d).

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

So, correct option is (b).

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

So, the correct option is (a).

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

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.

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

So, the correct option is (a).

The height and radius of the cone of which the frustum is a part are h_{1} and r_{3} respectively. If h_{2} and r_{2} are the heights and radius of the smaller base of the frustum respectively and h_{2} : h_{1} = 1: 2 then r_{2} : r_{1} is equal to

(a) 1 : 3

(b) 1 : 2

(c) 2 : 1

(d) 3 : 1

So, the correct option is (b).

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

So, the correct option is (c).

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

So, the correct option is (c).

## Chapter 14 - Surface Areas and Volumes Exercise 14.91

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 cm^{2}

(b) 2240 cm^{2}

(c) 880 cm^{2}

(d) 3120 cm^{2}

So, the correct option is (a).

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/cm^{2} is

(a) Rs. 1582.50

(b) Rs. 1724.50

(c) RS. 1683

(d) Rs. 1642

So, the correct option is (c)

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

So, the correct option is (b).

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

So, the correct option is (c).

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

So, the correct option is (c).

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

So, the correct option is (a).

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

So, the correct option is (b).

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

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

Correct option: (b)

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

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

Correct option: (a)

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

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. 4πr^{2}

b. 6πr^{2}

c. 3πr^{2}

d. 8πr^{2}

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 = 4πr^{2}

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

A spherical ball of radius r is melted to make 8 new identical balls each of radius r1. Then r : r_{1} =

a. 2 : 1

b. 1 : 2

c. 4 : 1

d. 1 : 4

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