The height of a right circular cone is 35 cm and the area of its curved surface is four times the area of its base. What is the volume of the cone (in $$10^{-3} m^3$$ and correct up to three decimal places)?

The height of the cone (h) = 35 cm

let the slant height is l  and radius r  

By the given cone $$\pi r l = 4 \pi r^2 $$

$$\Rightarrow l = 4 r $$

for a cone we have  $$ l^2 = r^2 + h^2 $$ 

put the value l = 4r 

then $$(4r)^2 = r^2 +35 $$ 

$$\Rightarrow r^2  = \dfrac {35\times 7}{ 3}$$

$$\Rightarrow r^2 = \dfrac{235}{3} $$

then volue of cone = $$ \dfrac {1}{3} \pi r^2 h $$ 

$$\Rightarrow \dfrac {1}{3} \times \dfrac {22}{7} \times {245}{3} \times 35 cm^2 $$

$$\Rightarrow 2.99444 cm ^2 $$

therefore option (C) 2.994  Ans