Question

The volume of a container measures 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

Answer 1

To find the empty space in the container, we first need to calculate the volume of a single tennis ball and then multiply that by the number of tennis balls to find the total volume occupied by the balls. Finally, we will subtract the total volume occupied by the tennis balls from the total volume of the container.

### Step 1: Calculate the volume of a single tennis ball

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

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

Where:
- \( \pi \) is approximately 3.14,
- \( r \) is the radius of the sphere.

Substituting the values:

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

Calculating \( (2.5)^3 \):

\[
(2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625 \text{ in}^3
\]

Now substitute into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 15.625
\]
\[
= \frac{4 \times 3.14 \times 15.625}{3}
\]
\[
= \frac{246.875}{3} \approx 82.2916667 \text{ in}^3
\]

### Step 2: Calculate the total volume of a dozen tennis balls

Since there are 12 tennis balls:

\[
\text{Total volume of tennis balls} = 12 \times 82.2916667 \approx 987.5 \text{ in}^3
\]

### Step 3: Calculate the empty space in the container

The total volume of the container is given as 3,200 in³. To find the empty space:

\[
\text{Empty space} = \text{Total volume of container} - \text{Total volume of tennis balls}
\]
\[
= 3200 - 987.5 = 2212.5 \text{ in}^3
\]

### Step 4: Round to the nearest whole number

Rounding \( 2212.5 \) to the nearest whole number gives:

\[
2213 \text{ in}^3
\]

Thus, the empty space in the container is approximately **2213 in³**.