Question

Ratio of $CSA$ & $TSA$ of cylinder is $1:2$, find volume If $T.S.A616c{m}^2$.

Answer 1

As we know that,

TSA of cylinder $=2\pi rh+2\pi r^2$

CSA of cylinder $=2\pi rh$

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

Now,

$\frac{CSA}{TSA}=\frac{1}{2}\left(\text{Given}\right)$

$\because TSA=616{cm}^2\left(\text{Given}\right)$

$\therefore CSA=\frac{1}{2}\times 616$

$\Rightarrow CSA=308{cm}^2$

Now,

$TSA=CSA+2\pi r^2$

$616-308=2\pi r^2$

$\Rightarrow r^2=\frac{308\times 7}{22\times 2}=49c{m}^2$

$\Rightarrow r=7cm$

Also,

$2\pi rh=2\pi r^2=308c{m}^2$

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

$\Rightarrow r=h$

Therefore,

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

$=\frac{22}{7}{r}^3(\because r=h)$

$=\frac{22}{7}\times {\left(7\right)}^3=1078{cm}^3$