The radius and height of a right circular cone are in the ratio 1: (2.4). If its curved surface area is 2502.5 cm$$^2$$, then what is its volume(Take $$\pi$$=$$\frac{22}{7}$$)

As per the above,

Let the radius is r and hight is h,

So, $$r:h=1:2.4$$

So, r=k and h=2.4k, l$$=\sqrt{k^2+(2.4k)^2}=2.6k$$

The curved surface area of the cylinder $$=2502.5 cm^2$$

So, the curved surface area of the cone $$\pi r l =2502.5 cm^2$$

$$\pi \times k\times 2.6k =2502.5 cm^2$$

$$\Rightarrow k^2=\dfrac{2502.5\times 7}{2.6\times 22}=306.25 cm^2$$

$$\Rightarrow k=\sqrt{306.25 cm^2}=17.5cm $$

Volume of the cone $$=\dfrac{\pi r^2 h}{3}=\dfrac{3.14 \times k\times 2.4 k}{3}$$

$$\Rightarrow =\dfrac{22 \times 17.5\times 17.5 \times 2.4\times 17.5}{3\times 7}=13475 cm^3$$