Question

If the volume of a cylinder of height $7cm$ is $448\pi c{m}^3$, find its lateral surface area and total surface area.

Answer 1

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

Height = $7cm$

$\therefore \pi r^{2}h=448\pi c{m}^3$

$\therefore r^2\times 7=448$

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

$\therefore r=\sqrt{64}=8cm$

$\therefore$ Lateral surface area = $2\pi rh$

$=2\pi \left(8\right)\left(7\right)$

$=112\pi cm=351.68cm$

$\therefore$ Total surface area = $2\pi r(h+r)$

$=112\pi (7+8)$

$=112\pi \times 15$

$=1680\pi c{m}^2$

$=5275.2c{m}^2$