Question

When given the diameter of a sphere, how can the volume be calculated? Describe the steps needed to find the volume.

Answer 1

To calculate the volume of a sphere when given the diameter, you can follow these steps:

1. **Find the Radius**: The radius (r) of the sphere is half of the diameter (d). Use the formula:
\[
r = \frac{d}{2}
\]

2. **Use the Volume Formula**: The formula for the volume (V) of a sphere is:
\[
V = \frac{4}{3} \pi r^3
\]
where \(\pi\) (pi) is approximately 3.14159.

3. **Substitute the Radius into the Volume Formula**: Once you have the radius, substitute it into the volume formula.

4. **Calculate the Volume**: Perform the calculations to find the volume.

### Example:
Let's go through an example step-by-step.

**Given Diameter**: 10 units

1. **Calculate the Radius**:
\[
r = \frac{10}{2} = 5 \text{ units}
\]

2. **Use the Volume Formula**:
\[
V = \frac{4}{3} \pi (5)^3
\]

3. **Calculate \(5^3\)**:
\[
5^3 = 125
\]

4. **Substitute Back into the Volume Formula**:
\[
V = \frac{4}{3} \pi (125)
\]

5. **Calculate**:
\[
V = \frac{500}{3} \pi \approx 523.6 \text{ cubic units}
\]

So, the volume of the sphere with a diameter of 10 units is approximately 523.6 cubic units.

You can use a calculator to get a more precise answer or to verify calculations as needed.