To measure the volume of a ball, we use 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:
- \( V \) is the volume
- \( r \) is the radius of the sphere
- \( \pi \) is a mathematical constant (approximately 3.14159)
Given that the diameter of the ball is \( 24 \) cm, the radius \( r \) would be half of the diameter:
[tex]\[ r = \frac{24}{2} = 12 \text{ cm} \][/tex]
Substitute the radius \( r = 12 \) cm into the volume formula:
[tex]\[ V = \frac{4}{3} \pi (12)^3 \][/tex]
Calculate \( 12^3 \):
[tex]\[ 12^3 = 12 \times 12 \times 12 = 1728 \][/tex]
Now, substitute \( 12^3 = 1728 \) back into the formula:
[tex]\[ V = \frac{4}{3} \pi \times 1728 \][/tex]
Thus, the correct equation that Sheena should set up to find the volume of the ball is:
[tex]\[ v = \frac{4}{3} \pi 12^3 \][/tex]
This equation correctly represents the volume of a sphere given the radius.
