Question

The volume of a cylinder is $150\pi cu.cm$ and its height is $6cm$. Find the areas of its total surface and lateral (curved) surface.

Answer 1

Volume of cylinder $=150\pi {cm}^3$

As we know that volume of the cylinder is given as-

$V=\pi r^{2}h$

$\therefore \pi r^{2}h=150\pi$

$\Rightarrow r^2=\frac{150}{6}$

$\Rightarrow r=\sqrt{25}=5$

Therefore,

Lateral surface area $=2\pi rh=2\times \pi \times 5\times 6=60\pi {cm}^2$

Total surface area $=2\pi r(r+h)=2\times \pi \times 5\times (5+6)=110\pi {cm}^2$