Question

The volume of a solid cylinder is $448\pi c{m}^3$ and height $7cm$. Find its lateral surface area and total surface area.

Answer 1

Let the radius of the base and height of the cylinder be r cm and h cm respectively. Then, $h=7cm$

Now, Volume = $448\pi c{m}^3$

$\pi r^{2}h=448\pi$

$r^2=\frac{448}{7}=64$

$r=8cm$

Therefore,

Lateral surface area $=2\pi rh=2\times \frac{22}{7}\times 8\times 7$

Lateral surface area $=352c{m}^2$

Total surface area $=2\pi r(r+h)=2\times \frac{22}{7}\times 8(7+8)$

Total surface area $=\frac{5280}{7}$

Total surface area$=754.28c{m}^2$