To determine the correct equation for calculating the volume of a sphere when given the diameter, let's go through the steps to set up this equation:
1. Identify the Diameter and Radius:
- The diameter of the ball is given as 24 cm.
- The radius [tex]\( r \)[/tex] of the ball is half of the diameter. So,
[tex]\[
r = \frac{24}{2} = 12 \text{ cm}
\][/tex]
2. Formula for the Volume of a Sphere:
- The formula for the volume [tex]\( V \)[/tex] of a sphere is:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
3. Substitute the Radius into the Formula:
- We substitute the radius (12 cm) into the formula:
[tex]\[
V = \frac{4}{3} \pi (12)^3
\][/tex]
Therefore, the correct setup for the equation to calculate the volume of the ball is:
[tex]\[
V = \frac{4}{3} \pi 12^3
\][/tex]
So, Sheena should use the following equation:
[tex]\[
V = \frac{4}{3} \pi 12^3
\][/tex]
This matches the last option in the provided choices:
[tex]\[
V = \frac{4}{3} \pi 12^3
\][/tex]
