Question

The radius and height of a cylinder are in ratio $7:2$. If the volume of the cylinder is $8316c{m}^3$, find the TSA of the cylinder.

Answer 1

The radius and height of a cylinder are in ratio $7:2$

Let ratio of radius and height of a cylinder are $7x$ and $2x$.

Volume of the cylinder $\left(V\right)=8316c{m}^3$

$\Rightarrow \pi r^{2}h=8316c{m}^3$

$\Rightarrow \frac{22}{7}\left(7x{)}^2\right(2x)=8316c{m}^3$

$\Rightarrow x^3=8316\times \frac{7}{22}\times \frac{1}{49}\times \frac{1}{2}c{m}^3$

$\Rightarrow x^3=27c{m}^3$

$\Rightarrow x=3cm$

Radius of the cylinder $=7\times 3cm=21cm$

Height of the cylinder $=2\times 3cm=6cm$

Total surface area of the cylinder $=2\pi r(r+h)$

$=2\times \frac{22}{7}\times 21cm(21cm+6cm)$

$=132cm\times 27cm$

$=3564c{m}^2$