Question

1. 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 will buy? a. 9.4 inches b. 4.7 inches c. 3.7 inches d. 7.4 inches

Explanation:

Step1: Find the volume of the new ball

The original volume is $434\ in^3$, and the new - ball has half the volume. So the volume of the new ball $V=\frac{434}{2}=217\ in^3$.

Step2: Recall the volume formula for a sphere

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

Step3: Solve for $r$

First, we can rewrite the equation as $r^{3}=\frac{217\times3}{4\pi}$. Then $r^{3}=\frac{651}{4\pi}$. Taking $\pi\approx3.14$, we have $r^{3}=\frac{651}{4\times3.14}=\frac{651}{12.56}\approx51.83$. So $r=\sqrt[3]{51.83}\approx3.7$.

Step4: Find the diameter $d$

Since the diameter $d = 2r$, and $r\approx3.7$ inches, then $d=2\times3.7 = 7.4$ inches.

Answer:

D. 7.4 inches