Question

The maximum volume of a cone that can be carved out of a solid hemisphere of radius r is

(a) $3{\mathrm{\pi r}}^2$

(b) $\frac{{\mathrm{\pi r}}^3}{3}$

(c) $\frac{{\mathrm{\pi r}}^2}{3}$

(d) $3{\mathrm{\pi r}}^3$

Answer 1

Radius of hemisphere = r

Therefore,

The radius of cone = r

and height h = r

Then,

Volume of cone

Hence, the correct answer is choice (b).