Question

Volume and curved surface area of a cylinder are $1650{cm}^3$ and $660{cm}^2$ respectively.Find the radius and height of the cylinder.

Answer 1

Let radius of cylinder be r. and height be h.
Given volume of cylinder $1650{cm}^3$
$\Rightarrow \pi r^{2}h=1650\dots .\left(i\right)$
Curved surface area of cylinder $=660{cm}^2$
$\Rightarrow 2\pi rh=660\dots \left(ii\right)$
On dividing (i) by (ii), we get
$\begin{array}{cc}\frac{\pi r^{2}h}{2\pi rh}& =\frac{1650}{660}\\ \frac{r}{2}& =\frac{5}{2}\end{array}$
$r=\frac{5\times 2}{2}$
$=5cm$
substituting this value of r in equation (ii), we get
$2\pi rh=660$
$2\times \frac{22}{7}\times 5\times h=660$
$\begin{array}{cc}h& =\frac{660\times 7}{2\times 22\times 5}\\ & =21cm\end{array}$
Hence, the radius is $5cm$ and height is $21cm$.