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## Chapter 13: Surface Areas and Volumes

#### TEXTBOOK’S EXERCISE – 13.7

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

Sol. (i) Here, r = 6 cm, h = 7 cm

Volume of the cone = 13 πr2h

= 1/3 × 22/7 × 6 × 6 × 7 cm3 = 264 cm3

(ii) Here, r = 3.5 cm, h = 12 cm

Volume of the cone = 13 πr2h

= 1/3 × 22/7 × 3.5 × 3.5 × 12 cm3 = 154 cm3

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

Sol. (i) Here, r = 7 cm, l = 25 cm

Volume of the conical vessel = 13 πr2h

= 13 × 22 7 × 7 × 7 × 24 cm3 = 1232 cm3

= 1232/1000 litres = 1.232 litres

(ii) Here, h = 12 cm, l = 13 cm

Volume of the conical vessel = 13 πr2h

= 1/3 × 22/7 × 5 × 5 × 12 cm3

3. The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. (Use π = 3.14)

Sol. (i) Here, h = 15 cm, volume = 1570 cm3

Volume of the cone = 13 πr2h

⇒ 1570 = 13 × 3.14 × r2 × 15

Hence, radius of the base = 10 cm

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

Sol. Here, h = 9 cm, volume = 48π cm3

Volume of the cone = 13 πr2h

⇒ 48π = 13 π × r2 × 9

⇒   r = 4

Hence, base diameter of the cone

= 2 × 4 cm = 8 cm

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