Question

the volume of a basketball is 434 in³. steve wants a ball with half the volume. what would be the approximate diameter of the ball steve would buy?
3.7 inches
4.7 inches
7.4 inches
8.4 inches

Explanation:

Step1: Find the new volume

The original volume of the basketball is $V_1 = 434$ in³. Steve wants a ball with half the volume, so the new volume $V_2=\frac{434}{2}=217$ in³.

Step2: Recall the volume - formula for a sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$. We know $V = V_2=217$ in³, so we have the equation $217=\frac{4}{3}\pi r^{3}$.

Step3: Solve for the radius $r$

First, we can rewrite the equation as $r^{3}=\frac{217\times3}{4\pi}$.
$r^{3}=\frac{651}{4\pi}$.
$r^{3}=\frac{651}{4\times3.14}\approx\frac{651}{12.56}\approx51.83$.
Then $r=\sqrt[3]{51.83}\approx3.73$ inches.

Step4: Find the diameter $d$

Since $d = 2r$, $d=2\times3.73 = 7.46\approx7.4$ inches.

Answer:

7.4 inches (closest to the calculated value among the options, assuming the closest option is the intended answer)