Question

A solid is in the shape of a cone standing on a hemisphere with both their diameters being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid. [Use π = 3.14]

Answer 1

Diameter of cone (r) = Diameter of hemisphere (r)

Height of cone (h) = Radius of cone = `1/2`cm

Volume of the solid = Volume of the cone + Volume of the hemisphere

= `1/3 πr^2h + 2/3 πr^3`

= `(πr^2)/3 (h + 2r)`

= `π/3(1/2)^2 (1/2 + 2 xx 1/2)`

= `π/(3 xx 4) (3/2) cm^3`

= `3.14/8 cm^3`

∴ Volume of the solid = 0.3925 cm³