Question

A solid metallic spherical ball of diameter $6$cm is melted and recast into a cone with diameter of the base as $12$cm. The height of the cone is _________.

• A. $2$cm
• B. $3$cm
• C. $4$cm
• D. $6$cm

Answer 1

The correct option is B $3$cm

Volume of the spherical ball $V_s=\frac{4}{3}\pi r^3=\frac{4}{3}{3}^3\pi =36\pi c{m}^3$

Volume of the cone made from sphere $V_c=\frac{1}{3}\pi r^{2}h=\frac{1}{3}{6}^2\times h\pi =12h\pi c{m}^3$

$\Rightarrow V_s=V_c\Rightarrow 36\pi =12h\pi \Rightarrow h=36/12=3cm$