To solve for the volume of the ball, Sheena needs to recognize that it's a sphere. The correct formula to find the volume [tex]\( V \)[/tex] of a sphere is:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
Given that the diameter of the ball is 24 cm, we can find the radius by dividing the diameter by 2:
[tex]\[ r = \frac{24}{2} = 12 \text{ cm} \][/tex]
Now, substitute [tex]\( r = 12 \text{ cm} \)[/tex] into the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi (12)^3 \][/tex]
To compare this with the options given, we can review each option for correctness:
1. [tex]\( V = \frac{1}{3} \pi 24^2(12) \)[/tex]
2. [tex]\( V = \frac{1}{3} \pi 12^2(24) \)[/tex]
3. [tex]\( V = \frac{4}{3} \pi 24^3 \)[/tex]
4. [tex]\( V = \frac{4}{3} \pi 12^3 \)[/tex]
By direct comparison, the correct option that represents the volume of the sphere with a radius of 12 cm should be:
[tex]\[ V = \frac{4}{3} \pi 12^3 \][/tex]
Hence, Sheena should use the formula:
[tex]\[ V = \frac{4}{3} \pi 12^3 \][/tex]
Therefore, the right equation for Sheena is:
[tex]\[ \boxed{V = \frac{4}{3} \pi 12^3} \][/tex]
