Question

sheena wants to measure the volume of a ball that is 24 cm across. how should she set up her equation?
\\( v = \frac{1}{3}\pi24^2(12) \\)
\\( v = \frac{1}{3}\pi12^2(24) \\)
\\( v = \frac{4}{3}\pi24^3 \\)
\\( v = \frac{4}{3}\pi12^3 \\)

Explanation:

Step1: Recall the volume formula for a sphere

The volume \( V \) of a sphere is given by the formula \( V = \frac{4}{3}\pi r^3 \), where \( r \) is the radius of the sphere.

Step2: Determine the radius of the ball

The ball (sphere) has a diameter of 24 cm. The radius \( r \) is half of the diameter, so \( r=\frac{24}{2}=12 \) cm.

Step3: Substitute the radius into the volume formula

Substitute \( r = 12 \) into the formula \( V=\frac{4}{3}\pi r^3 \). We get \( V=\frac{4}{3}\pi(12)^3 \), which is \( V = \frac{4}{3}\pi12^{3} \).

Answer:

\( V = \frac{4}{3}\pi12^{3} \) (the last option)