Find the radius of a sphere whose surface area is 616 `cm^(2)`.

Answer

To find the radius of a sphere whose surface area is 616 cm², we can follow these steps:

### Step-by-Step Solution:

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

2. **Substitute the given surface area into the formula.**
We know the surface area \( S \) is 616 cm². Therefore, we can set up the equation:
\[ 4 \pi r^2 = 616 \]

3. **Use the value of \( \pi \).**
For calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this value into the equation gives:
\[ 4 \times \frac{22}{7} \times r^2 = 616 \]

4. **Simplify the equation.**
To isolate \( r^2 \), we first need to rearrange the equation:
\[ r^2 = \frac{616 \times 7}{4 \times 22} \]

5. **Calculate \( 4 \times 22 \).**
Calculate \( 4 \times 22 \):
\[ 4 \times 22 = 88 \]

6. **Now substitute back into the equation.**
The equation now looks like:
\[ r^2 = \frac{616 \times 7}{88} \]

7. **Calculate \( \frac{616}{88} \).**
Dividing \( 616 \) by \( 88 \):
\[ 616 \div 88 = 7 \]

8. **Now substitute this value back into the equation.**
So, we have:
\[ r^2 = 7 \times 7 = 49 \]

9. **Find the value of \( r \).**
To find \( r \), take the square root of \( 49 \):
\[ r = \sqrt{49} = 7 \]

10. **State the final answer with the unit.**
Therefore, the radius of the sphere is:
\[ r = 7 \text{ cm} \]