Question

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

Answer 1

Surface area of solid cylinder = 231 $c{m}^2$

and curved surface area = $\frac{2}{3}\times 231c{m}^2$

= 154 $c{m}^2$

Now $2\pi$ rh = 154 ...........(i)

and 2 $\pi rh+2\pi r^2$ = 231

Subtracting, $2\pi r^2$ = 231 - 154 = 77

$2\times \frac{22}{7}\times r^2$ = 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

Now, from (i) $2\times \frac{22}{7}\times \frac{7}{2}h$ = 154

22h = 154 $\Rightarrow h=\frac{154}{22}=7$

$\therefore$ Volume = $\pi r^{2}h=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 7c{m}^3$

=$\frac{539}{2}=269.5c{m}^2$