Question

question 1 - 9 (nda 912 cea 4.9) 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 wants? o 7.4 inches o 4.7 inches o 9.4 inches o 3.7 inches

Explanation:

Step1: Recall volume formula for sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius. Let the volume of the original basketball be $V_1=\frac{4}{3}\pi r_1^{3}=434$ in³. The new - ball has volume $V_2=\frac{V_1}{2}=\frac{434}{2} = 217$ in³.

Step2: Solve for radius of new ball

We know that $V_2=\frac{4}{3}\pi r_2^{3}=217$. First, we can solve for $r_2^{3}$:
$r_2^{3}=\frac{217\times3}{4\pi}$.
$r_2^{3}=\frac{651}{4\pi}$.
Taking $\pi\approx3.14$, we have $r_2^{3}=\frac{651}{4\times3.14}=\frac{651}{12.56}\approx51.83$.
Then $r_2=\sqrt[3]{51.83}\approx3.73$ inches.

Step3: Calculate diameter of new ball

The diameter $d = 2r$. So $d = 2r_2$.
$d=2\times3.73 = 7.46\approx7.4$ inches.

Answer:

7.4 inches