The total surface area of a hemisphere of radius 7 cm is

Options

A. `(588 pi) cm^(2)`
B. `(392 pi) cm^(2)`
C. `(147 pi) cm^(2)`
D. `(98 pi ) cm^(2)`

Explanation

To find the total surface area of a hemisphere with a radius of 7 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Total Surface Area of a Hemisphere**:
The total surface area (TSA) of a hemisphere is given by the formula:
\[ \text{TSA} = 3\pi r^2 \]
where \( r \) is the radius of the hemisphere.

2. **Identify the Radius**:
From the question, we know that the radius \( r \) is 7 cm.

3. **Substitute the Radius into the Formula**:
Now, we will substitute \( r = 7 \) cm into the TSA formula:
\[ \text{TSA} = 3\pi (7)^2 \]

4. **Calculate \( r^2 \)**:
First, calculate \( 7^2 \):
\[ 7^2 = 49 \]

5. **Multiply by 3 and \(\pi\)**:
Now substitute \( 49 \) back into the equation:
\[ \text{TSA} = 3\pi \times 49 \]
\[ \text{TSA} = 147\pi \]

6. **Final Answer**:
Therefore, the total surface area of the hemisphere is:
\[ \text{TSA} = 147\pi \text{ cm}^2 \]

### Conclusion:
The total surface area of the hemisphere of radius 7 cm is \( 147\pi \text{ cm}^2 \).