Question

What is the total surface area of a hemisphere of radius R?

• A. \(\pi R^2\)
• B. \(2\pi R^2\)
• C. \(3\pi R^2\)
• D. \(4\pi R^2\)

Hint:

Don't confuse the total surface area (\(3\pi R^2\)) with the curved surface area (\(2\pi R^2\)). The "total" area includes the flat circular top.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The total surface area (TSA) of a hemisphere is the sum of its curved surface area (CSA) and the area of its flat circular base.

Step 2: Key Formula or Approach:
1. The curved surface area of a hemisphere is half the surface area of a full sphere: \(CSA_{hemisphere} = \frac{1}{2} (4\pi R^2) = 2\pi R^2\).
2. The area of the circular base is given by the formula for the area of a circle: \(A_{base} = \pi R^2\).
3. The total surface area is the sum of these two areas: \(TSA = CSA + A_{base}\).

Step 3: Detailed Explanation:
\[ TSA_{hemisphere} = (2\pi R^2) + (\pi R^2) \] \[ TSA_{hemisphere} = 3\pi R^2 \]

Step 4: Final Answer:
The total surface area of a hemisphere of radius R is \(3\pi R^2\).