Question

A sphere of radius 4 cm is melted and recast into the shape of a cylinder of radius 8 cm. What is the height of the cylinder formed?

• A. 1.33 cm
• B. 3.21 cm
• C. 0.95 cm
• D. 2.22 cm

Answer 1

The correct option is A

1.33 cm

Given, radius of sphere, r = 4 cm
radius of cylinder, R = 8 cm
Let height of the cylinder be h cm.

Volume of sphere
$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (4{)}^3=\frac{256}{3}\pi c{m}^3$

Volume of the cylinder
$=\pi R^{2}h=\pi \times (8{)}^2\times h=64\pi h$

In the process of melting and recasting, the volume of the solids remain the same.
So, volume of the sphere = volume of the cylinder
$\Rightarrow \frac{256}{3}\pi =64\pi h$
$\Rightarrow \frac{256}{3}=64h$
$\Rightarrow h=\frac{256}{3\times 64}$
$\Rightarrow h=1.33cm$

Therefore, height of the cylinder = 1.33 cm