To determine the volume of the Bluetooth speaker, which is in the shape of a cube, we use the formula for the volume of a cube:
\[ V = s^3 \]
where \( s \) is the length of an edge. Given that the edge length is 4.5 inches:
\[ V = (4.5 , \text{inches})^3 = 4.5 \times 4.5 \times 4.5 \]
Calculating this step-by-step:
\[ 4.5 \times 4.5 = 20.25 \] \[ 20.25 \times 4.5 = 91.125 \]
Thus, the volume of the speaker is:
\[ \text{Volume of the speaker} = 91.125 , \text{cubic inches} \]
Next, we determine the volume of the container shaped as a square prism using the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Given that the base area is 25 square inches and the height is 6.25 inches:
\[ V = 25 , \text{square inches} \times 6.25 , \text{inches} = 156.25 , \text{cubic inches} \]
Thus, the volume of the container is:
\[ \text{Volume of the container} = 156.25 , \text{cubic inches} \]
Finally, to find the amount of empty space remaining in the container after placing the speaker inside, we subtract the volume of the speaker from the volume of the container:
\[ \text{Empty Space} = \text{Volume of the Container} - \text{Volume of the Speaker} \]
Calculating this:
\[ \text{Empty Space} = 156.25 , \text{cubic inches} - 91.125 , \text{cubic inches} = 65.125 , \text{cubic inches} \]
Summarizing all the answers:
- Volume of the speaker: 91.125 cubic inches
- Volume of the container: 156.25 cubic inches
- Empty space remaining: 65.125 cubic inches