Question

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

Answer 1

Total surface area$=231$sq.cm

Curved Surface area$=\frac{2}{3}$ of T.S.A

$\Rightarrow 2\pi rh=\frac{2}{3}\times 231$

$\Rightarrow 2\pi rh=154$sqcm

Total surface area$=231$sq.cm

$\Rightarrow 2\pi r(r+h)=231$sq.cm

$\Rightarrow 2\pi r^2+2\pi rh=231$sq.cm

$\Rightarrow 2\pi r^2+154=231$sq.cm

$\Rightarrow 2\pi r^2=231-154=77$

$\Rightarrow 2\times \frac{22}{7}\times r^2=77$

$\Rightarrow r^2=\frac{49}{4}$

$\therefore r=\sqrt{\frac{49}{4}}=\frac{7}{2}=3.5$cm

Curved surface area$=154$sq.cm

Also, $2\times \frac{22}{7}\times 3.5h=154$

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

Volume of the cylinder

$=\pi r^{2}h=\frac{22}{7}\times 3.5\times 3.5\times 7=269.5$cu.cm

$\therefore$ Volume of the cylinder$=269.5$cu.cm