Question

The ratio of radius and height of a cylinder is $1:3$. If volume of cylinder is $3234c{m}^3$ then find total surface are cylinder.

Answer 1

$\frac{r}{h}=\frac{1}{3}$ $\therefore h=3r$

Volume of cylinder $=\pi r^{2}h$

$3234=\frac{22}{7}\times r^2\times 3r$

$\therefore r^3=343$

$r=7cm$

$\therefore$ Total surface area of cylinder

$=2\pi r^2+2\pi rh$

$=2\pi r(r+h)$

$=2\times \frac{22}{7}\times 7(7+3\times 7)(\because h=3r)$

$=2\times 22\times 7\times 4$

$=1232c{m}^2$