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

Q. Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius $r$.

Q. Find the maximum volume of a cone that can be out of a solid hemisphere of radius $r$.

Q. STATEMENT - 1 : The volume of largest sphere that can be carved out from
cube of side a cm is $\frac{1}{6}\pi a^3$
STATEMENT - 2 : Volume of sphere is $\frac{4}{3}\pi r^3$ and for largest sphere to carved from cube radius of sphere $=$ side of cube

Q. The cone of maximum size is carved out from a cube of edge $14cm.$ Find the Volume of the remaining solid after the cone is carved out

Q. Find the volume of largest possible cone can be curved out from hemisphere of radius 'r'.