Question

A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.

Answer 1

Given, radius of cone = radius of hemisphere

= r

= 7 cm

Height of cone (h) = 2 × radius

= 2 × 7

= 14 cm

Volume of solid = Volume of cone + Volume of hemisphere

Volume of solid (V) = `1/3 πr^2h + 2/3 πr^3`

= `1/3 πr^2(2r) + 2/3 πr^3`  ...(∵ h = 2r)

= `2/3 πr^3 + 2/3 πr^3`

= `4/3 πr^3`

= `4/3 xx 22/7 xx 7 xx 7 xx 7`

= `4312/3`

= 1437.33 cm³