Question

A solid sphere of radius $x$ cm is melted and recast into a shape of a solid cone of radius $x$ cm. The height of the cone is:

• A. $3x$ cm
• B. $x$ cm
• C. $4x$ cm
• D. $2x$ cm

Answer 1

Answer: (C)

$4x$ cm

Let the height of the cone be $h$ $cm$

Volume remains constant after the recast.

Therefore, volume of cone $=$ volume of sphere so,

$\frac{1}{3}\pi x^{2}h=\frac{4}{3}\pi x^3{x}^{2}h=4x^{3}h=4x$