Question

The ratio between curved surface area and total surface area of a cylinder is $2:3$. If the total surface area be $924c{m}^2$, find the volume of the cylinder.

• A. $2156c{m}^3$
• B. $1256c{m}^3$
• C. $1265c{m}^3$
• D. $1862c{m}^3$

Answer 1

The correct option is A $2156c{m}^3$

Given $\frac{\Pi rh}{2\Pi (r+h)}=\frac{2}{3}\Rightarrow \frac{h}{r+h}=\frac{2}{3}$
Or 3h=2r+2h or h=2r
TSA=924 Then $2\Pi r(r+h)=924\Rightarrow 2\Pi r(r+2r)=924\Rightarrow 6\times \Pi r^2=924\Rightarrow r=7cm$ And h=14Tthe volume of the cylinder=$\Pi r^{2}h=\frac{22}{7}(7{)}^2\times 14=2156c{m}^3$