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.

Since the conical cavity is hollowed out from the cube,

Volume of remaining solid = volume of cube - volume of cone

Now,

For Cube

Side, a = 7 cm

Volume of cube = (7)³ = 343 cm³

[ As Volume of cube = a³,

where a = side of cube]

For cone

Radius, r = 3 cm

Height, h = 7 cm

Volume of cone

[As volume of cone

where r = radius and h = height

Volume of remaining solid = 343 - 66 = 277 cm³