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 \{3[/tex]
D. [tex]v = \frac{4}{3} \pi 12^3[/tex]



Answer :

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.