Question

question 1 - 3 (ma 912 gr 4 5) 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
7.4 inches
4.7 inches
3.7 inches
9.4 inches

Explanation:

Step1: Find the volume of the new ball

The volume of the new ball is half of 434 in³, so $V=\frac{434}{2}=217$ in³.

Step2: Recall the volume - formula for a sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$.

Step3: Solve for the radius $r$

We have $217=\frac{4}{3}\pi r^{3}$. First, we can rewrite it as $r^{3}=\frac{217\times3}{4\pi}$. Then $r^{3}=\frac{651}{4\pi}$. Using $\pi\approx3.14$, we get $r^{3}=\frac{651}{4\times3.14}=\frac{651}{12.56}\approx51.83$. Taking the cube - root of both sides, $r\approx3.73$ inches.

Step4: Find the diameter $d$

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

Answer:

7.4 inches