# A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $$\pi$$.

Volume of the solid = Volume of the cone + Volume of the hemisphere

$$= \ \frac{1}{3} \pi r^2 h \ + \ \frac{2}{3} \pi R^3$$

$$= \ \frac{1}{3} \pi r^2 \ × \ r \ + \ \frac{2}{3} \pi r^3$$ [$$\because$$ h = r and R = r]

$$= \ \frac{ \pi}{3}r^3(1 \ + \ 2) \ = \ \pi r^3$$

$$= \ \pi(1)^3 \ = \ \pi$$ cm3 [$$\because$$ r = 1 cm]