Question

An empty cone of radius 3 cm and height 12 cm is filled with ice-cream such that the lower part of the cone which is `(1/6)^"th"` of the volume of the cone is unfilled (empty) but a hemisphere is formed on the top. Find the volume of the ice-cream.

Answer 1

A cone of radius (r) = 3 cm and height (h) = 12 cm

The cone is filled with ice-cream except for `1/6^"th"` of the cone’s volume, which is empty.

Also, a hemisphere with a radius of 3 cm is added on top.

We must find total volume of ice-cream.

Volume of cone = `1/3πr^2h`

= `1/3π xx 3 xx 3 xx 12`

= 36π cm³

Volume of ice-cream in the cone = `5/6 xx 36π cm^3`

= 30π cm³

Volume of ice-cream in the hemispherical = `2/3πr^3`

= `2/3π xx 3 xx 3 xx 3`

= 18π cm³

Total volume of the ice-cream = (30π + 18π)

= 48π

= 150.86 cm³ (approx.)