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 determine the volume of a sphere, you need to use the formula:

[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]

where [tex]\( r \)[/tex] is the radius of the sphere.

1. The diameter of the ball is given as 24 cm.
2. The radius is half of the diameter, so:
[tex]\[ r = \frac{24}{2} = 12 \text{ cm} \][/tex]

3. We substitute the radius into the volume formula:
[tex]\[ V = \frac{4}{3} \pi (12)^3 \][/tex]

Thus, the correct equation to use for finding the volume is:

[tex]\[ V = \frac{4}{3} \pi 12^3 \][/tex]