Question

The cost of painting the total outside surface of a closed cylinder at Rs$3perc{m}^2$ is Rs$2772$. If the height of the cylinder is $2$ times the radius, then find its volume.

Answer 1

Given:
Cost of painting the total area of cylinder at
Rs $3perc{m}^2$ is Rs$2772$.

Let the radius of cylinder be $r$ and height $\left(h\right)$ be $2r$.

Total surface area
$=\frac{Totalcostofpainting}{Costperc{m}^2}$

$=\frac{2772}{3}=924c{m}^2$

Since, T.S.A of the cylinder
$=2\pi r(r+h)$

$\Rightarrow 2\pi r(r+2r)=924$

$\Rightarrow 6\pi r^2=924$

$\Rightarrow r^2=\frac{924\times 7}{6\times 22}=49$

$\Rightarrow r=7cm$

$\Rightarrow h=2r=14cm$

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

$=\frac{22}{7}\times (7{)}^2\times 14$

$=2156c{m}^3$

Hence, the volume of the cylinder is $2156c{m}^3$.