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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.

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Solution:

Given that, side of a solid cube (a) = 7cm 

Height of conical cavity i.e., cone, h = 7 cm

Since, the height of conical cavity and the side of cube is equal that means the conical cavity fit vertically in the cube.

Radius of conical cavity i.e., cone, r = 3 cm

⇒ Diameter = 2 x r = 2 x 3= 6 cm

Since, the diameter is less than the side of a cube that means the base of a conical cavity is

not fit in horizontal face of cube.

Hence, the required volume of solid is 277 cm³

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