Question

The ratio between the curved surface area and the total surface area of right cylinder is 2:3 and the total surface area is 924 $c{m}^2.$ What is the volume of the cylinder?

• A. 2156 cc
• B. 2183 cc
• C. 2492 cc
• D. None of these

Answer 1

The correct option is A 2156 cc

Total surface Area : $\frac{2\pi r^2+2\pi rh}{2\pi rh}=\frac{3}{2}\Rightarrow 1+\frac{r}{h}=\frac{3}{2}\Rightarrow \frac{r}{h}=\frac{1}{2}\Rightarrow h=2r$

TSA : $(2\pi r^2+2\pi rh)=924\Rightarrow (2\pi r^2+2\pi r\times 2r$) = 924

$\Rightarrow$ r = 7 and h = 14
Volume =$\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 14=2156$