The curved surface area of a hemisphere is 8π cm², then its radius is:

Concept

The curved (lateral) surface of a hemisphere is exactly half of a full sphere's surface. A full sphere has surface area 4πr2; therefore the curved surface area of a hemisphere is CSA = 2πr2. This is the only quantity asked here, so the flat circular base is not counted.

Application

1. Write the formula: CSA = 2πr2.

2. Set it equal to the given value: 2πr2 = 8π.

3. Divide both sides by 2π to isolate r2: r2 = 4.

4. Take the positive square root (a length is non-negative): r = 2 cm.

Cross-check

Substitute r = 2 back into the formula: 2π(2)2 = 2π × 4 = 8π cm2, which matches the given curved surface area, confirming r = 2 cm.