Question

The volume of the greatest right circular cone, which can be cut from a cube of side 4 cm is __________.

Answer 1

The greatest right circular cone will be such that the diameter of the base of the cone will be equal to the side of the cube and the height of the cone will be equal to the side of the cube.

Radius of the greatest right circular cone which can be cut from the given cube, r = $\frac{4}{2}$ = 2 cm

Height of the greatest right circular cone which can be cut from the given cube, h = 4 cm

∴ Volume of the greatest right circular cone which can be cut from the given cube

$$\begin{gathered} =\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ =\frac{1}{3}\mathrm{\pi }\times 2^2\times 4 \\ =\frac{16}{3}\mathrm{\pi }{\mathrm{cm}}^3 \end{gathered}$$

The volume of the greatest right circular cone, which can be cut from a cube of side 4 cm is $\underline{\frac{16}{3}\mathrm{\pi }{\mathrm{cm}}^3}$.