RD SHARMA SOLUTION CHAPTER -20 Surface Area and Volume of a Right Circular Cone| CLASS 9TH MATHEMATICS-EDUGROWN

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

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6Find its curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.Solution 6

Question 7Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.Solution 7

Question 8

Solution 8

Question 9The curved surface area of a cone is 4070 cm² and its diameter is 70 cm. What is its slant height? (Use  = 22/7).Solution 9

Question 10

Solution 10

Question 11A 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

Question 12Find 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

Question 13

Solution 13

Question 14

Solution 14

Question 15Curved 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 = 

    Thus, the radius of circular end of the cone is 7 cm.

(ii)    Total surface area of cone = CSA of cone + Area of base
                     =

Thus, the total surface area of the cone is 462 .

Question 16The 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

Question 17A 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

Question 18

Solution 18

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  = 3.14).

Solution 19Height (h) of conical tent = 8 m
    Radius (r) of base of tent = 6 m
    Slant height (l) of tent = 
    CSA of conical tent =  = (3.14  6  10)  = 188.4 

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)  3] m = 188.4 
    L – 0.2 m = 62.8 m
    L = 63 m

    Thus, the length of the tarpaulin sheet will be 63 m.Question 20

Solution 20

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

Question 22

Solution 22

Question 23

Solution 23

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

Question 1Find 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 

(ii)   Radius (r) of cone = 3.5 cm
       Height (h) of cone = 12 cm
       Volume of cone  
(iii)

Question 2Find 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  
       Volume of cone  
       Capacity of the conical vessel =  litres= 1.232 litres(ii)    Height (h) of cone = 12 cm
        Slant height (l) of cone = 13 cm        
        Radius (r) of cone 
        Volume of cone   = 314.28 cm³
        Capacity of the conical vessel = litres =  litres.

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 9A 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  = 3.14).Solution 9

Question 10

Solution 10

Question 11A 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

Question 12

Solution 12

Question 13The 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 coneSolution 13(i)    Radius of cone =   =14 cm
       Let height of cone be h.
       Volume of cone = 9856 cm³
        h = 48 cm       Thus, the height of the cone is 48 cm. (ii)   Slant height (l) of cone  
       Thus, the slant height of the cone is 50 cm. (iii)    CSA of cone = rl = Question 14

A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?Solution 14Radius (r) of pit =
Depth (h) of pit = 12 m
Volume of pit =Capacity of the pit = (38.5  1) kilolitres = 38.5 kilolitres

Question 15Monica 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