Find the surface area of a sphere of radius 7 cm.

Answer

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

### Step-by-Step Solution:

1. **Identify the formula for the surface area of a sphere.**
The formula for the surface area \( A \) of a sphere is given by:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.

2. **Substitute the radius into the formula.**
Given that the radius \( r = 7 \) cm, we can substitute this value into the formula:
\[ A = 4\pi (7)^2 \]

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

4. **Multiply by \( 4\pi \).**
Now substitute \( 49 \) back into the surface area formula:
\[ A = 4\pi \times 49 \]

5. **Calculate \( 4 \times 49 \).**
Multiply \( 4 \) by \( 49 \):
\[ 4 \times 49 = 196 \]

6. **Final expression for surface area.**
Therefore, the surface area can be expressed as:
\[ A = 196\pi \text{ cm}^2 \]

7. **Approximate the value using \( \pi \approx \frac{22}{7} \).**
If we want to approximate the surface area using \( \pi \approx \frac{22}{7} \):
\[ A \approx 196 \times \frac{22}{7} \]

8. **Calculate the approximate surface area.**
To calculate:
\[ A \approx 196 \times \frac{22}{7} = \frac{4312}{7} \approx 616 \text{ cm}^2 \]

### Final Answer:
The surface area of the sphere is \( 196\pi \) cm² or approximately \( 616 \) cm².