From a cube of edge 14 cm, a cone of maximum size is carved out. Find the volume of the remaining material.
From a cube of edge 14 cm, a cone of maximum size is carved out. Find the volume of the remaining material.

Given edge of the cube, a = 14 cm

Radius of the cone, r = 14/2 = 7 cm

Height of the cone, h = 14 cm

Volume of the cube = a3

= 143

= 14×14×14

= 2744 cm3

Volume of the cone = (1/3)r2h

= (1/3)×(22/7)×72×14

= 22×7×14/3

= 2156/3 cm3

Volume of the remaining material = Volume of the cube- Volume of the cone

= 2744-2156/3

= (3×2744-2156)/3

= (8232 – 2156)/3

= 6076/3

Hence the volume of the remaining material is  2025.33