Question

If the volume of a semi-sphere is 18π cm³, what will be the total surface area of that semi-sphere?
1. 27π cm²
2. 18π cm²
3. 24π cm²
4. 21π cm²

Answer 1

Correct Answer - Option 1 : 27π cm²

Given

The volume of a semi - sphere = 18π cm3

Formula used:

The volume of the semi-sphere = (2/3)πr³

The total area of the semi-sphere = 3πr2 

Calculation

According to the question,

The volume of the semi-sphere = (2/3)πr3

⇒ 18π = (2/3)πr3

⇒ 9 = r³/3

⇒ r³ = 27

⇒ r = 3.

Now, The total surface area of the semi-sphere = 3πr2 

⇒ 3πr²  

⇒ 3π × 3² 

⇒ 27π

 ∴ The total surface area of that semi-sphere is 27π cm²