Question

The curved surface area of a cylinder is $1320c{m}^2$ and its base has a diameter $21cm.$ Find the volume of the cylinder.

Answer 1

Given: The diameter of the cylinder is $21cm.$

Radius of the cylinder, $r=\frac{21}{2}=10.5cm$

Let height of the cylinder be $hcm$
Since the curved surface area has been known, we can calculate ${}^{\prime }{h}^{\prime }$ by the equation given below:
The curved surface area of the cylinder $=2\pi rh$
$\Rightarrow 2\pi rh=1320c{m}^2$

$\Rightarrow 2\times \frac{22}{7}\times \frac{21}{2}\times h=1320c{m}^2$

$\Rightarrow 66h=1320c{m}^2$​​

$\Rightarrow h=\frac{1320}{66}c{m}^2$

$\Rightarrow h=20cm$

​​$\therefore$ Volume of the cylinder $\left(V\right)=\pi r^{2}h$

​$V=\frac{22}{7}\left(10.5cm{)}^2\right(20cm)$​

$V=6930c{m}^3$