Question

The diameter of a metallic sphere is $4.2\text{cm}$. It is melted and recast into a right circular cone of height $8.4\text{cm}$. Find the radius of the base of the cone.

Answer 1

Sphere: Diameter $\left(d\right)=4.2\text{cm}\Rightarrow r=\frac{4.2}{2}=2.1\text{cm}$
Cone: $h=8.4\text{cm}$
Volume of sphere$=$ Volume of cone
$\frac{4}{3}\pi r_s^3=\frac{1}{3}\pi r_c^2{h}_c$
$\therefore r_c^2=\frac{\frac{4}{3}\pi r_s^3}{\frac{1}{3}\pi h_c}=\frac{4\times 2.1\times 2.1\times 2.1}{8.4}=2.1\times 2.1$
$r_c=\sqrt{2.1\times 2.1}=2.1\text{cm}$
$\therefore$ Radius of base of the cone $=2.1\text{cm}$.