Question

A solid hemisphere of radius 3 cm is melted to cast a right circular cone of the same base as that of hemisphere. Find the height of the cone.

Answer 1

volume of hemisphere = volume of CONE
2/3 * 22/ 7 * [3]^3 = 1/3 * 22/7 * (3)^2 *H
1188/21 = 198H/21
1188 = 198 H
H = 1188/198
= 6cm

Answer 2

$\huge\mathfrak{Solution:}$

Since the base of the hemisphere and cone are equal

Therefore, radius of the base of the cone = 3 cm

Suppose height of the cone = h cm

Since cone is casted by melting the hemisphere

Therefore, volume of the hemisphere = volume of the cone

Therefore, 1/2 × 4/3 × pi × r^3 = 1/3 × pi × r^2 × h

or 2 × r^3 = r^2 × h

or 2 × (3)^3 = (3)^2 × h

or h = 2 × 3 × 3 × 3 / 3 × 3 = 6

Hence, height of the cone = 6 cm

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