Question

A bluetooth speaker is in the shape of a cube with an edge length of 4.5 inches.



(3 points)
**Do not round the answers.**

Determine the volume of the speaker.
cubic inches

The speaker is sold in a container in the shape of a square prism with a base of 25 square inches and a height of 6.25 inches.

Determine the volume of the container.
cubic inches

How much empty space remains in the container after the speaker is placed in the package?
cubic inches

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Answer 1

To solve the problems, we will use the formulas for the volume of a cube and a rectangular prism.

1. **Volume of the Bluetooth Speaker (Cube):**

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

\[
V = s^3
\]

where \( s \) is the edge length. Given:

\[
s = 4.5 \text{ inches}
\]

So,

\[
V = 4.5^3 = 4.5 \times 4.5 \times 4.5
\]

Calculating this:

\[
4.5 \times 4.5 = 20.25
\]
\[
20.25 \times 4.5 = 91.125
\]

Thus, the volume of the speaker is:

\[
\text{Volume of speaker} = 91.125 \text{ cubic inches}
\]

2. **Volume of the Container (Square Prism):**

The formula for the volume \( V \) of a rectangular prism (in this case, a square prism) is given by:

\[
V = \text{base area} \times \text{height}
\]

Given the base area is 25 square inches and the height is 6.25 inches:

\[
V = 25 \times 6.25
\]

Calculating this:

\[
25 \times 6.25 = 156.25
\]

Thus, the volume of the container is:

\[
\text{Volume of container} = 156.25 \text{ cubic inches}
\]

3. **Empty Space in the Container After Placing the Speaker:**

To find the empty space in the container after placing the speaker inside, subtract the volume of the speaker from the volume of the container:

\[
\text{Empty space} = \text{Volume of container} - \text{Volume of speaker}
\]

Substituting in the values we have:

\[
\text{Empty space} = 156.25 - 91.125
\]

Calculating this:

\[
156.25 - 91.125 = 65.125
\]

Thus, the empty space remaining in the container after placing the speaker is:

\[
\text{Empty space} = 65.125 \text{ cubic inches}
\]

**Summary of Results:**
- Volume of the speaker: **91.125 cubic inches**
- Volume of the container: **156.25 cubic inches**
- Empty space remaining: **65.125 cubic inches**