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.
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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 [because r = 3 cm]
or h = 2 × 3 × 3 × 3 / 3 × 3 = 6
Hence, height of the cone = 6 cm
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