The total surface area of a hemispher is 75$\pi cm^2$. Find the radius.

Analyze the question: We're given the total surface area of a hemisphere, 75π cm², and asked to find the radius.

Concept: A solid hemisphere has two surfaces:

• Curved surface: 2πr²
• Flat circular base: πr²

So the total surface area = 2πr² + πr² = 3πr²

(Note: if the question meant only the curved surface, it would be 2πr². "Total surface area" includes the flat base.)

Solution:

3πr² = 75π

Divide both sides by π:

3r² = 75

r² = 25

r = 5 cm

Check: 3π(5)² = 3π(25) = 75π ✓

Answer: The radius is 5.0 cm, which is option A.

Tip: Remember "total surface area of a hemisphere = 3πr²" (curved 2πr² + base πr²). In exams, watch the wording: "curved surface area" means 2πr², while "total surface area" means 3πr². Many students lose marks by forgetting the flat base.