Question

a manufacturer makes solid rubber balls. it takes 111.3 cubic inches of rubber to make 3 equally - sized balls. rounding to the nearest hundredth of an inch, what is the diameter of one of the balls? the diameter of a ball is approximately inches.

Explanation:

Step1: Find volume of one ball

The volume of 3 balls is 111.3 cubic - inches. So the volume of one ball $V=\frac{111.3}{3}=37.1$ cubic - inches.

Step2: Use the volume formula for a sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$. We know $V = 37.1$, so we can solve for $r$.
$37.1=\frac{4}{3}\pi r^{3}$
First, multiply both sides by $\frac{3}{4\pi}$:
$r^{3}=\frac{37.1\times3}{4\pi}=\frac{111.3}{4\pi}$
$r^{3}=\frac{111.3}{4\times3.14159}\approx\frac{111.3}{12.56636}\approx8.86$
Then, take the cube - root of both sides: $r=\sqrt[3]{8.86}\approx2.07$ inches.

Step3: Find the diameter

The diameter $d = 2r$. So $d=2\times2.07 = 4.14$ inches.

Answer:

4.14