Question

Total surface area of a solid hemisphere with radius $r$ will be

• A. $2\pi r^2$
• B. $4\pi r^2$
• C. $3\pi r^2$
• D. $6\pi r^2$

Hint:

For hollow hemispheres, use only the curved surface area ($2\pi r^2$), but for solid ones, add the base area as well ($3\pi r^2$).

Answer 1

The Correct Option is C

Step 1: Recall the formula for a hemisphere.
For a hemisphere, there are two surface areas to consider: 1. Curved surface area (CSA) = $2\pi r^2$
2. Base area (circular base) = $\pi r^2$
Step 2: Add both to get the total surface area.
\[ \text{Total surface area} = 2\pi r^2 + \pi r^2 = 3\pi r^2 \] Step 3: Conclusion.
Hence, the total surface area of a solid hemisphere is $3\pi r^2$.