Question

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​

Answer 1

Answer:

height h = 1/3πr2h

Slant height of the cone, l = √r² + h²

i) Radius of the conical vessel, r = 7cm

Slant height of the conical vessel, l = 25cm

Height of the conical vessel, h = √l² - r²

= √(25)² - (7)²

= √625 - 49

= √576

h = 24 cm

Capacity of the conical vessel = 1/3 πr²h

= 1/3 × 22/7 × 7 cm × 7 cm × 24 cm

= 1232 cm³

= 1232 × (1/1000L) [∵ 1000 cm³ = 1litre]

= 1.232 litres

ii) Height of the conical vessel, h = 7cm

Slant height of the conical vessel, l = 13cm

Radius of the conical vessel, r = √l² - h²

= √(13)² - (12)²

= √169 -144

= √25

r = 5 cm

Capacity of the conical vessel = 1/3πr²h

= 1/3 × 22/7 × 5 cm × 5 cm × 12 cm

= 2200/7 cm³

= 2200/7 × 1/1000 l [∵ 1000 cm³ = 1litre]

= 11/35 litres