The area of the base of a solid cone is 616 $$cm^{2}$$. If the height of the cone is 15 cm, then what is the volume of this cone?

The area of the base of a solid cone is 616 $$cm^{2}$$.

area of the base of a solid cone = $$\pi\ \times\ \left(radius\right)^2$$ = 616    Eq.(i)

If the height of the cone is 15 cm.

Volume of the cone = $$\frac{1}{3}\times\ \pi\ \times\ \left(radius\right)^2\times\ height$$

= $$\frac{1}{3}\times\ \pi\ \times\ \left(radius\right)^2\times\ 15$$

Put Eq.(i) in the above equation.

= $$\frac{1}{3}\times616\times\ 15$$

= $$616\times5$$

= 3080 $$cm^{3}$$