To solve the problems, we will use the formulas for the volume of a cube and a rectangular prism.
- 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:
\[ \text{Volume of speaker} = 91.125 \text{ cubic inches} \]
- 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:
\[ \text{Volume of container} = 156.25 \text{ cubic inches} \]
- 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