Question

.If the volume and curved surface area of a hemisphere are numerically equal, then the diameter of hemisphere will be *
2 अंक
4cm
6cm
3.5cm
3cm​

Answer 1

Answer;

6 cm

Given:

• The volume and curved surface area of a hemisphere are numerically equal.

To Find:

• The diameter of the hemisphere

Solution:

For a hemisphere, where r is radius:

Volume = (2/3)πr³

Curved surface area = 2πr²

According to the question:

Volume = Curved surface area

➡ (2/3) πr³ = 2πr²

➡ (2/3)r³ = 2r²

➡ 2/3r = 2

➡ r = 2 × 3/2

➡ r = 3

Radius = r = 3

Diameter = 2r = 3(2) = 6

Diameter is 6 units, so option (B) 6cm is correct.