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