Question

A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid.

Answer 1

The diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm.

Therefore, radius = r = 7/2 cm

Its curved surface area = 2πr²

Surface area of the top of the resulting solid = Surface area of the top face of the cube − Area of the base of the hemisphere

Surface area of the cube = 5 × (side)² = 5 × 49 = 245 cm² ………. (iii)

Total area of resulting solid = 245 + 10.5 + 77 = 332.5 cm²