# Solution of Chapter 20. Surface Area and Volume of a Right Circular Cone (RD Sharma - Mathematics Book)

## Exercise 20.1

1

Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.

2

The radius of a cone is 5 cm and vertical height is 12 cm. Find the area of the curved surface.

3

The radius of a cone is 7 cm and area of curved surface is 176 cm2. Find the slant height.

4

The height of a cone is 21 cm. Find the area of the base if the slant height is 28 cm.

5

Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.

6

Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm.

7

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

8

The area of the curved surface of a cone is 60π cm2. If the slant height of the cone be 8 cm, find the radius of the base.

9

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

10

The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use π=22/7)

11

A Joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

12

Find the ratio of the curved surface areas of two cones if their diameters of the bases are equal and slant heights are in the ratio 4 : 3.

13

There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.

14

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

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.

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.

17

A conical tent is 10 m high and the radius of its base is 24 m. Find the 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.

18

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

19

A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.

20

The circumference of the base of a 10 m height conical tent is 44 metres. Calculate the length of canvas used in making the tent if width of canvas is 2 m. (Use π=22/7).

21

What length of tarpaulin 3 m wide will be required to make a conical tent of height 8 m and base radius 6 m? Assume that the extra length of material will be required for stitching margins and wastage in cutting is approximately 20 cm. (Use π=3.14).

22

A bus stop is barricaded from the remaining part of the road, by using 50 hollow cone made of recycled card-board. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs. 12 per m2. What will be the cost of painting all these cones. (Use π=3.14 and = 1.02).

23

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 is to the height of each as 3 : 4.

## Exercise 20.2

1

Find the volume of a 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.

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.

3

Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Find the ratio of their volumes.

4

The radius and the height of a rightr circular cone are in the ratio 5 : 12. If its volume is 314 cubic metre, find the slant height and the radius (Use π =3.14).

5

The radius and height of a right circular cone are in the ratio 5 : 12 and its volume is 2512 cubic cm. Find the slant height and radius of the cone. (Use π =3.14)

6

The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. Find the ratio of their vertical heights.

7

A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3 : 1.

8

If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?

9

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π =3.14)

10

Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm, supposing the material of which it is made weighs 10 grams per cubic cm.

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.

12

Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.

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.

14

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

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 wastage incurred while cutting, amounts to approximately 1 m2. Find the volume of the tent that can be made with it.

## CCE - Formative Assessment

1

The height of a cone is 15 cm. If its volume is 500π cm3, then find the radius of its base.

2

If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.

3

If the height and slant height of a cone are 21 cm and 28 cm respectively. Find its volume.

4

The height of a conical vessel is 3.5 cm. If its capacity is 3.3 litres of milk. Find the diameter of its base.

5

If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm2, find its radius.

6

Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.

7

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

8

Find the length of cloth used in making a conical pandal of height 100 m and base radius 240 m, if the cloth is 100π m wide.

1

The number of surfaces of a cone has, is

2

The area of the curved surface of a cone of radius 2r and slant height , is

3

The total surface area of a cone of radius and length 2l, is

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

5

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

6

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

7

If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is

8

If the volume 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

9

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

10

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

11

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

12

A right circular 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

13

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

14

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

15

If h, S and V denote respectively the height, curved surface area and volume of a right circular cone, then 3πVh3-S2h2+9V2 is equal to