Question

From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Answer 1

From the figure, we get,

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

For Cube

Side, a = 7 cm

We know that,

Volume of cube = a³, where a = side of cube

Volume of cube = (7)³ = 343 cm³

For cone

Radius, r = 3 cm

Height, h = 7 cm

Volume of cone = `1/3 π"r"^2"h"` 

= `1/3 π(3)^(2)7` 

= `3 xx 22/7 xx 7`

= 66 cm³

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

= 343 – 66

= 277 cm³