Question

A metallic sphere of radius $4.2$ cm is melted and recast into the shape of a cylinder of radius $6$ cm. Find the height of the cylinder.

Answer 1

Given:
Radius ($r_1$) of hemisphere $=4.2$ cm
Radius ($r_2$) of cylinder $=6$ cm
Height (h) = ?
The object fromed by recasting the hemisphere will be same in volume.
So, $\text{Volume of sphere = Volume of cylinder}$
$\frac{4}{3}\pi r_1^3=\pi r_2^{2}h$

$⟹\frac{4}{3}\pi \times (4.2{)}^3=\pi (6{)}^{2}h$

$⟹\frac{4}{3}\times \frac{4.2\times 4.2\times 4.2}{36}=h$

$h=(1.4{)}^3=2.74$ cm

Therefore, the height of cylinder so formed will be $2.74$ cm.