Question

The volume of a container measures 3,200 in.3
3
,
200

in.
3
and contains a dozen tennis balls. Each tennis ball has a radius of 2.5 in. How much space in the container is empty? Use 3.14 as an approximation for pi. Round to the nearest whole number, if necessary.(1 point)
in.3
its not 2416 i cant give anything else

Answer 1

To find out how much space is empty in the container, we first need to calculate the volume of one tennis ball and then the total volume of 12 tennis balls.

1. **Volume of One Tennis Ball**:
The formula for the volume \( V \) of a sphere is:

\[
V = \frac{4}{3} \pi r^3
\]

Where \( r \) is the radius. Given that the radius of each tennis ball is 2.5 inches:

\[
V = \frac{4}{3} \times 3.14 \times (2.5)^3
\]

First, calculate \( (2.5)^3 \):

\[
(2.5)^3 = 15.625
\]

Now plug this value back into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 15.625
\]

Calculate \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.18867
\]

Now multiply by 15.625:

\[
V \approx 4.18867 \times 15.625 \approx 65.4415 \text{ in}^3
\]

The approximate volume of one tennis ball is **65.44 in³**.

2. **Total Volume of 12 Tennis Balls**:
Multiply the volume of one ball by 12:

\[
V_{\text{total}} = 65.44 \times 12 \approx 785.28 \text{ in}^3
\]

3. **Empty Space in the Container**:
Now we subtract the total volume of the tennis balls from the volume of the container:

\[
V_{\text{empty}} = 3200 - 785.28 \approx 2414.72 \text{ in}^3
\]

Rounding to the nearest whole number:

\[
V_{\text{empty}} \approx 2415 \text{ in}^3
\]

Thus, the amount of empty space in the container is approximately **2415 in³**.