Question

If the radius of hemisphere will be tripled then the lateral surface area of new hemisphere is how many times than the previous one?
1. 6 times
2. 4 times
3. 12 times
4. 9 times

Answer 1

Correct Answer - Option 4 : 9 times

Given:

A hemisphere is given whose radius will be tripled

Formula used:

Lateral surface area of hemisphere is 2πr²

where, r = radius

Calculations:

Let the radius of the hemisphere is r

According to question, we have

The new radius of the hemisphere is 3r

Lateral surface area of hemisphere is 2πr2

⇒ Lateral surface area of new hemisphere = 2 × π × (3r)²

Lateral surface area of new hemisphere/Lateral surface of hemisphere

⇒ (3r)²/r²

⇒ 9r²/r²

⇒ 9/1

∴ The lateral surface area of new hemisphere is 9 times than the previous one