A solid metallic sphere of radius 12 cm is melted and recast into a cone having diameter of the base as 12 cm. What is the height of the cone?

192 cm

We know that,

The volume of a sphere = \(\frac{4}{3}\) πr³

The volume of a cone = \(\frac{1}{3}\) πr²h

We have,

The radius of the sphere = 12 cm

Diameter of the base of the cone = 12 cm

Now,

The volume of the sphere = Volume of the cone

\(\frac{4}{3}\) π(12)³= \(\frac{1}{3}\) π(6)²h

= 4 × 12³ = π6²h

= 4 × 48 = h

= h = 192