To find the volume of a ball (which is a sphere) with a given diameter, you should follow these steps:
1. Determine the radius of the ball:
The radius (r) of a sphere is half of its diameter. So if the diameter is 6 inches:
[tex]\[
\text{radius} = \frac{\text{diameter}}{2} = \frac{6 \text{ inches}}{2} = 3 \text{ inches}
\][/tex]
2. Find the formula for the volume of a sphere:
The volume (V) of a sphere is given by the formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\(\pi\)[/tex] is approximately 3.14159 and [tex]\(r\)[/tex] is the radius of the sphere.
3. Substitute the radius into the formula:
Use the radius we calculated:
[tex]\[
V = \frac{4}{3} \pi (3 \text{ inches})^3
\][/tex]
4. Calculate the radius cubed:
[tex]\[
3^3 = 3 \times 3 \times 3 = 27 \text{ cubic inches}
\][/tex]
5. Multiply by [tex]\(\pi\)[/tex]:
[tex]\[
\pi \times 27 \approx 3.14159 \times 27 \approx 84.823
\][/tex]
6. Multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[
\frac{4}{3} \times 84.823 \approx 113.097
\][/tex]
Therefore, the volume of the ball with a diameter of 6 inches is approximately [tex]\(113.1\)[/tex] cubic inches (rounded to one decimal place).
