Question

The internal and external radii of a hollow sphere are $3cm$ and $5cm$ respectively. The sphere is melted to form a solid cylinder of height $2\frac{2}{3}cm.$ Find the diameter and curved surface area of the cylinder.

Answer 1

Volume of the hollow sphere $=\frac{4}{3}\pi \times (R^3-r^3)$

$=\frac{4}{3}\pi \times (5³-3³)$

$=\frac{392\pi }{3}c{m}^3$

Since it is melted to form a cylinder

So, Volume of cylinder = volume of the sphere

$\Rightarrow \pi r^{2}h=\frac{392\pi }{3}c{m}^3$

$\Rightarrow r²=\frac{392\times 3}{32\times 3}$

$=12.25$

$\Rightarrow r=\sqrt{12.25}=3.5cm$

$\therefore$ Diameter of cylinder $=3.5\times 2=7cm$