Question

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

• A. $r$
• B. $2r$
• C. $r^2$
• D. $\frac{r}{2}$

Answer 1

The correct option is B $2r$

Radius of sphere $=r$

Volume of sphere $=\frac{4}{3}\pi r^3$

Let radius of the base of cone be $R$ and height is $h=r$

Now volume of cone $=\frac{1}{3}\pi r^{2}h$ $=\frac{1}{3}\pi R^{2}r$

But Volume of cone $=$ Volume of sphere

$\Rightarrow \frac{1}{3}\pi R^{2}r=\frac{4}{3}\pi r^3\Rightarrow R^2=4r^2\Rightarrow R=2r$

Hence, radius of base of cone $=2r$