RD SHARMA Solutions for Class 9 Maths Chapter 20 - Surface Areas and Volume of A Right Circular Cone

Page / Exercise

Chapter 20 - Surface Areas and Volume of A Right Circular Cone Exercise 20.24

Question 1

The number of surfaces of a cone has, is

(a) 1

(b) 2

(c) 3

(d) 4

Solution 1

A cone has two surfaces as follows: one curved surface and another bottom surface.

Hence, correct option is (b).

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 4

A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio

(a) 9 : 1

(b) 1 : 9

(c) 3 : 1

(d) 1 : 3

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 6

If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is

(a) 1 : 5

(b) 5 : 4

(c) 5 : 16

(d) 25 : 64

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 7

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is

(a) 2 : 1

(b) 4 : 1

(c) 8 : 1

(d) 1 : 1

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Chapter 20 - Surface Areas and Volume of A Right Circular Cone Exercise 20.25

Question 1

If the height and radius of a cone of volume V are doubled, then the volume of the cone, is

(a) 3V

(b) 4V

(c) 6V

(d) 8V

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 2

The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height, is

(a) 1 : 3

(b) 3 : 1

(c) 4 : 3

(d) 3 : 4

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 3

A right circular cylinder cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is

(a) 3 : 5

(b) 2 : 5

(c) 3 : 1

(d) 1 : 3

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 4

The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, the ratio of their curved surface areas, is

(a) 4 : 5

(b) 25 : 16

(c) 16 : 25

(d) 5 : 4

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 5

If the heights of two cones are in the ratio of 1 : 4 and the radii of their bases are in the ratio 4 : 1, then the ratio of their volumes is

(a) 1 : 2

(b) 2 : 3

(c) 3 : 4

(d) 4 : 1

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 6

The  slant height of a cone is increased by 10%. If the radius remains the same, the curved surface area is increased by 

(a) 10%

(b) 12.1%

(c) 20%

(d) 21%

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 7

The height of a solid cone is 12 cm and the area of the circular base is 64∏ cm2. A plane parallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, thee area of the base of the new cone so formed is

(a) 9∏ cm2

(b) 16∏ cm2

(c) 25∏ cm2

(d) 36∏ cm2

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 8

If the base radius and the height of a right circular cone are increased by 20%, then the percentage increase in volume is approximately

(a) 60

(b) 68

(c) 73

(d) 78

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 9

If h, S and V denote respectively the height, curved surface area and volume of a right circular cone, then 3∏Vh3 - S2h+ 9V2 is equal to

(a) 8

(b) 0

(c) 4∏

(d) 32∏2

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

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 upper and lower part is

(a) 1 : 2

(b) 2 : 1

(c) 1 : 7

(d) 1 : 8

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Chapter 20 - Surface Areas and Volume of A Right Circular Cone Exercise Ex. 20.1

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 6
Find its curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 7
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 9
The curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. What is its slant height? (Use Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone = 22/7).
Solution 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 11
A joker's cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
Solution 11
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 12
Find the ratio of the curved surface area of two cones if their diameters of the bases are equal and slant heights are in the ratio 4:3.
Solution 12
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 13
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 13
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 14
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 14
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 15
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.
Solution 15
(i)    Slant height of cone = 14 cm
    Let radius of circular end of cone be r.
    CSA of cone = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone    
    Thus, the radius of circular end of the cone is 7 cm.

(ii)    Total surface area of cone = CSA of cone + Area of base
                     =Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Thus, the total surface area of the cone is 462 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone.
    

                      


Question 16
The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 m2.
Solution 16
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 17
A conical tent is 10 m high and the radius of its base is 24 m. Find slant height of the tent. If the cost of 1 m2 canvas is Rs 70, find the cost of the canvas required to make the tent,
Solution 17
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 19

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone = 3.14).

Solution 19
Height (h) of conical tent = 8 m
    Radius (r) of base of tent = 6 m
    Slant height (l) of tent = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone    
    CSA of conical tent = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone = (3.14 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular ConeRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone 10) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone = 188.4 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Let length of tarpaulin sheet required be L.
As 20 cm will be wasted so, effective length will be (L - 0.2 m)
Breadth of tarpaulin = 3 m
Area of sheet = CSA of tent
    [(L - 0.2 m) Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone 3] m = 188.4 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
    L - 0.2 m = 62.8 m
    L = 63 m
   
    Thus, the length of the tarpaulin sheet will be 63 m.
Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 21

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the radius of each to the height of each is 3:4.

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Solution 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Question 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Solution 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone

Chapter 20 - Surface Areas and Volume of A Right Circular Cone Exercise Ex. 20.2

Question 1
Find the volume of the right circular cone with

(i) radius 6 cm, height 7 cm

(ii) radius 3.5 cm, height 12 cm

(iii) height 21 cm and slant height 28 cm.
Solution 1
(i)    Radius (r) of cone = 6 cm
       Height (h) of cone = 7 cm
       Volume of cone Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone  

(ii)   Radius (r) of cone = 3.5 cm
       Height (h) of cone = 12 cm
       Volume of cone  Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone 
(iii)
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 2
Find the capacity in litres of a conical vessel with
(i)    radius 7 cm, slant height 25 cm
(ii)   height 12 cm, slant height 13 cm

Solution 2
(i)    Radius (r) of cone = 7 cm
       Slant height (l) of cone = 25 cm
       Height (h) of cone  Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone 
       Volume of cone  Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
       Capacity of the conical vessel = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone litres= 1.232 litres
(ii)    Height (h) of cone = 12 cm
        Slant height (l) of cone = 13 cm
        
        Radius (r) of cone Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
        Volume of cone   Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone= 314.28 cm3
        Capacity of the conical vessel = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Conelitres = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone litres.

Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 9
A heap of wheat is in the form of a cone of diameter 9 m and height is 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (use Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone = 3.14).
Solution 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 11
A right angled triangle of which the sides containing the right angle are 6.3 cm and 10 cm in length, is made to turn round on the longer side. Find the volume of the solid, thus generated. Also, find its curved surface area.
Solution 11
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 12
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Solution 12
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 13
The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find

(i) height of the cone

(ii) slant height of the cone

(iii) curved surface area of the cone
Solution 13
(i)    Radius of cone =  Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone =14 cm
       Let height of cone be h.
       Volume of cone = 9856 cm3
      Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone 
       h = 48 cm
       Thus, the height of the cone is 48 cm.
 
(ii)   Slant height (l) of cone  Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
       Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone     
       Thus, the slant height of the cone is 50 cm.
 
(iii)    CSA of cone = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Conerl = Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Question 14

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

Solution 14
Radius (r) of pit =Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone 
Depth (h) of pit = 12 m
Volume of pit =Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular ConeCapacity of the pit = (38.5 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone 1) kilolitres = 38.5 kilolitres

Question 15
Monica has a piece of canvas whose area is 551 m2. She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with it.
Solution 15
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Surface Areas And Volume Of A Right Circular Cone