Question

If the area of the base of a cone is 770 $c{m}^2$and the curved surface area is 814 $c{m}^2$ then its volume is

• A. $616\sqrt{5}c{m}^3$
• B. $616/\sqrt{5}c{m}^3$
• C. $616\sqrt{3}c{m}^3$
• D. $616\sqrt{2}c{m}^3$

Answer 1

The correct option is A $616\sqrt{5}c{m}^3$

Given area of base of cone is 770 sq cm and curved surface area is 814 sq cm

Let radius of cone is r

$\therefore \pi r^2=770\Rightarrow r^2=\frac{770}{\pi }\Rightarrow r=\sqrt{\frac{770}{\pi }}$

$\therefore \pi rl=814\Rightarrow l=\frac{814}{\pi r}$

Then volume of cone =$\frac{1}{3}\pi r^{2}l=\frac{1}{3}\times \frac{770}{\pi }\times \frac{814}{\pi r}=616\sqrt{5}c{m}^3$