Question

A solid cylinder has a total surface area of $231c{m}^2$. Its curved surface area is $\frac{2}{3}$ of the total surface area. Find the volume of the cylinder.

Answer 1

Total surface area of a solid cylinder = Curved surface area = $\frac{2}{3}$ of 231 $c{m}^2$
= 2 $\times$ 77 = 154 $c{m}^2$
and area of two circular faces = 231- 154 = 77 $c{m}^2$
Let r be the radius, then
2 $\pi r^2$ = 77 $\Rightarrow$ 2 $\times \frac{22}{7}\times r^2$ =77
$r^2=\frac{77\times 7}{2\times 22}=\frac{49}{4}={\left(\frac{7}{2}\right)}^2$
$\therefore r=\frac{7}{2}$ cm
Curved surface area = 2 $\pi$ rh
$\therefore 2\pi rh$ = 154
$\Rightarrow 2\times \frac{22}{7}\times \frac{7}{2}h=154\Rightarrow 22h=154$
h= $\frac{154}{22}$ = 7 cm
Now volume = $\pi r^2$h
= $\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 7c{m}^3=\frac{539}{2}$
= 269.5 $c{m}^3$