The total surface area of a solid hemisphere of radius r is

Options

A. `pi r^2`
B. `2pi r^2`
C. `3pi r^2`
D. `4pi r^2`

Answer

To find the total surface area of a solid hemisphere of radius \( r \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Shape**: A solid hemisphere consists of a curved surface and a circular base.

2. **Identify the Components**:
- The curved surface area of the hemisphere.
- The area of the circular base.

3. **Calculate the Curved Surface Area**:
- The formula for the curved surface area of a hemisphere is given by:
\[ \text{Curved Surface Area} = 2\pi r^2 \]

4. **Calculate the Area of the Circular Base**:
- The formula for the area of a circle is:
\[ \text{Base Area} = \pi r^2 \]

5. **Add the Areas Together**:
- To find the total surface area of the hemisphere, we add the curved surface area and the base area:
\[ \text{Total Surface Area} = \text{Curved Surface Area} + \text{Base Area} \]
\[ \text{Total Surface Area} = 2\pi r^2 + \pi r^2 \]

6. **Simplify the Expression**:
- Combine the terms:
\[ \text{Total Surface Area} = 3\pi r^2 \]

7. **Conclusion**:
- Therefore, the total surface area of a solid hemisphere of radius \( r \) is:
\[ \text{Total Surface Area} = 3\pi r^2 \]

### Final Answer:
The total surface area of a solid hemisphere of radius \( r \) is \( 3\pi r^2 \).