Question

Total surface area of a solid hemisphere with radius \(r\) will be

• A. \(\frac{2}{3} \pi r^2\)
• B. \(2\pi r^2\)
• C. \(3\pi r^2\)
• D. \(4\pi r^2\)

Hint:

For a hemisphere, always add the base area \(\pi r^2\) to the curved surface area \(2\pi r^2\) to get total surface area.

Answer 1

The Correct Option is C

Step 1: Recall the formula for total surface area (TSA) of a solid hemisphere.
\[ \text{TSA} = \text{Curved Surface Area (CSA)} + \text{Base Area} \]
Step 2: Substitute the formulas.
\[ \text{CSA} = 2\pi r^2, \quad \text{Base Area} = \pi r^2 \] \[ \text{TSA} = 2\pi r^2 + \pi r^2 = 3\pi r^2 \]
Step 3: Conclusion.
Hence, the total surface area of a solid hemisphere is \(3\pi r^2\).