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

Answer 1

To find the empty space in the container, we first need to calculate the total volume of the tennis balls and then subtract that volume from the volume of the container.

1. **Calculate the volume of one tennis ball:**

The formula for the volume \( V \) of a sphere is given by:

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

Given that the radius \( r \) of each tennis ball is 2.5 inches, we substitute into the formula:

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

Calculating \( (2.5)^3 \):

\[
(2.5)^3 = 15.625
\]

Now substituting this value into the volume formula:

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

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

First, calculate \( 4 \times 3.14 \):

\[
4 \times 3.14 = 12.56
\]

Now, calculate \( 12.56 \times 15.625 \):

\[
12.56 \times 15.625 \approx 196.09375
\]

Finally, divide by 3:

\[
V \approx \frac{196.09375}{3} \approx 65.36458333 \text{ in}^3
\]

Thus, the volume of one tennis ball is approximately \( 65.36 \text{ in}^3 \).

2. **Calculate the volume of a dozen (12) tennis balls:**

\[
\text{Volume of 12 tennis balls} = 12 \times 65.36 \approx 784.32 \text{ in}^3
\]

3. **Calculate the empty space in the container:**

The volume of the container is \( 3,200 \text{ in}^3 \). Therefore, empty space in the container is:

\[
\text{Empty space} = \text{Volume of container} - \text{Volume of 12 tennis balls}
\]

\[
\text{Empty space} = 3200 - 784.32 \approx 2415.68 \text{ in}^3
\]

Rounding to the nearest whole number:

\[
\text{Empty space} \approx 2416 \text{ in}^3
\]

Therefore, the amount of empty space in the container is approximately **2416 in³**. If this is not satisfactory, please clarify or provide additional context to your question.