Sheena wants to measure the volume of a ball that is 24 cm across. How should she set up her equation?

A. [tex]V=\frac{1}{3} \pi 24^2(12)[/tex]
B. [tex]V=\frac{1}{3} \pi 12^2(24)[/tex]
C. [tex]V=\frac{4}{3} \pi 24^3[/tex]
D. [tex]V=\frac{4}{3} \pi 12^3[/tex]



Answer :

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]