Question

The volume of a cylinder of height 8 cm is $1232c{m}^3$. Find its curved surface area and the total surface area.

Answer 1

Volume of cylinder $=1232c{m}^3$

height (h)=8 cm

Let r be the radius, then

$\pi r^{2}h=1232$

$\frac{22}{7}\times r^2\times 8=1232$

$\Rightarrow r^2=\frac{1232\times 7}{22\times 8}$

$\Rightarrow r^2=49=(7{)}^2$

$\Rightarrow r=7cm$

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

$=2\times \frac{22}{7}\times 7\times 8=352c{m}^2$

and total surface area $=2\pi r(r+h)$

$=2\times \frac{22}{7}\times 7(7+8)c{m}^2=44\times 15=660c{m}^2$