The curved surface area of a hemisphere is 32π cm², then its radius is:

Concept

A hemisphere is half of a sphere. Its curved (lateral) surface area counts only the dome — the rounded part — and is given by CSA = 2πr2, where r is the radius. The flat circular base, πr2, is added only for the TOTAL surface area, 3πr2.

Application

1. Write the curved-surface-area relation: 2πr2 = 32π.

2. Divide both sides by 2π: r2 = 32π ÷ 2π = 16.

3. Take the positive square root (a radius is positive): r = √16 = 4 cm.

Cross-check

Substitute back: 2π(4)2 = 2π × 16 = 32π cm2, which matches the given curved surface area. So r = 4 cm.