If the surface area of sphere is `616 cm^(2)` , its diameter (in cm) is

Options

A. 7
B. 14
C. 28
D. 56

Explanation

To find the diameter of a sphere given its surface area, we can follow these steps:

### Step-by-Step Solution:

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

2. **Set up the equation with the given surface area**:
We know the surface area \( A \) is \( 616 \, \text{cm}^2 \). Therefore, we can write:
\[ 4\pi r^2 = 616 \]

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

4. **Simplify the equation**:
First, multiply \( 4 \) and \( \frac{22}{7} \):
\[ \frac{88}{7} r^2 = 616 \]

5. **Isolate \( r^2 \)**:
To isolate \( r^2 \), multiply both sides by \( \frac{7}{88} \):
\[ r^2 = 616 \times \frac{7}{88} \]

6. **Calculate \( 616 \div 88 \)**:
Simplifying \( 616 \div 88 \) gives:
\[ 616 \div 88 = 7 \]
Therefore, we have:
\[ r^2 = 7 \times 7 = 49 \]

7. **Find the radius \( r \)**:
Taking the square root of both sides gives:
\[ r = \sqrt{49} = 7 \, \text{cm} \]

8. **Calculate the diameter**:
The diameter \( d \) of the sphere is twice the radius:
\[ d = 2r = 2 \times 7 = 14 \, \text{cm} \]

### Final Answer:
The diameter of the sphere is \( 14 \, \text{cm} \).