Question

The curved surface area of a cylindrical pillar is $264m^2$ and its volume is $924m^3$. Find the diameter and the height of the pillar.

Answer 1

Given: The ratio of $C.S.A$ is $264m^2$ and its volume is $924m^3$.

Let, the radius of the cylinder be r and height be $h$.

$\because$ The curved surface area $=264c{m}^2$
$\Rightarrow 2\pi rh=264\dots \left(1\right)$
$\Rightarrow 2\times \frac{22}{7}\times r\times h=264$
$\Rightarrow rh=\frac{264\times 7}{2\times 22}=42$

Now, volume of the cylinder $=\pi r^{2}h=924$
$\Rightarrow \pi r^{2}h=924\dots \left(2\right)$

Dividing $\left(2\right)$ by $\left(1\right)$, we get
$\frac{\pi r^{2}h}{2\pi rh}=\frac{924}{264}$
$\Rightarrow \frac{r}{2}=\frac{7}{2}$
$\Rightarrow r=7\dots \left(3\right)$

Diameter $=2r=14m$
Put the value of $\left(3\right)$ in $\left(1\right)$, we get
$\Rightarrow h=\frac{264}{2\times \frac{22}{7}\times 7}=6m$

Hence, the base diameter and the height of the cylinder are $14m$ and $6m$ respectively.