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

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 will not fit in horizontal face of cube.

volume of cube$$=a^3$$

$$=7^3=343$$

and volume of conical cavity = $$\frac{1}{3}πr^2h$$
= $$\frac{1}{3}×\frac{22}{7}×3×3×7$$
= $$66cm^3$$

Therefore volume of remaining solid = volume of cube-volume of conical cavity
 $$343-66=277cm^3$$

Hence, the required volume of solid is 277 cm³