Question

The largest cone is curved out from one face of solid cube of side 21 cm.Find the volume of the remaining solid.

Answer 1

Solution:

Given that,

The radius of the largest possible cone is carved out of a solid cube is equal to the half of the side of the cube.

Diameter of the cone = 21 cm

Radius of the cone = 10.5 cm

The height of the cone is equal to the side of the cube.

Volume of the cube = $a^3={21}^3=9261c{m}^3---\left(1\right)$

Volume of the cone = $\frac{1}{3}\times \pi r^{2}h=\frac{1}{3}\times \pi \times {10.5}^2\times 21$

$=22\times {10.5}^2$

$=2425.5c{m}^3$

Volume of the remaining solid = Volume of cube – Volume of cone

V = $9261-2425.5$

V = $6835.5c{m}^3$