Class nine Maths NCERT Sol Surface Areas Volumes
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