Question

A solid metallic cone of radius 12 cm and height 48 cm was recast into a sphere. Radius of the sphere is

• A. 24 cm
• B. 12 cm
• C. 74 cm
• D. 15 cm

Answer 1

The correct option is B 12 cm

Given: Radius of the metallic cone, r = 12 cm
Height of the metallic cone, h = 48 cm

Volume of cone
= $\frac{1}{3}\pi r^{2}h$

Let R be the radius of sphere.

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

Now, volume of sphere = Volume of cone
$\Rightarrow$ $\frac{4}{3}\pi R^3=\frac{1}{3}\pi r^{2}h$
$\Rightarrow$ $R^3=\frac{r^{2}h}{4}$
$\Rightarrow$ $R^3=\frac{{12}^2\times 48}{4}$
$\Rightarrow$ $R^3={12}^3$
R = 12 cm