A metallic sphere of radius 6 cm is melted and recast into a cone of…

The correct answer is Option (2) → 54 cm

When the metal is melted and recast, its amount does not change, so the volume of the cone equals the volume of the sphere. The volume of a sphere of radius \(r\) is \(\frac{4}{3}\pi r^{3}\), and that of a cone of radius \(r\) and height \(h\) is \(\frac{1}{3}\pi r^{2}h\).

• Volume of the sphere: \(\displaystyle\frac{4}{3}\pi\times6^{3}=288\pi\,\mathrm{cm^3}\)

• Volume of the cone, set equal to it: \(\displaystyle\frac{1}{3}\pi\times4^{2}\times h=288\pi\)

• So \(16h=864\), and the height of the cone is \(h=54\) cm