Question

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

• A. 2.744 cm
• B. 4.818 cm
• C. 5.822 cm
• D. 6.136 cm

Answer 1

The correct option is A 2.744 cm

Radius of metallic sphere = r = 4.2 cm

Radius of cylinder = $r_1$ = 6 cm

Let height of cylinder = h cm

Since the metallic sphere of radius 4.2 cm is melted and recast into a cylinder of radius 6 cm, the volume of the metallic sphere is equal to the volume of the cylinder.

$\Rightarrow \frac{4}{3}\pi r^3=\pi \left(r_1^2\right)h$

$\Rightarrow \frac{4}{3}\times 4.2\times 4.2\times 4.2=6\times 6\times h$

$\Rightarrow h=\frac{4}{3}\times \frac{4.2\times 4.2\times 4.2}{6\times 6}$

$\Rightarrow h=2.744cm$