Question
A delivery truck service needs to transport 75 boxes. The boxes are all cubes with a side length of 18 in. How much space will the service need to transport the boxes? Use the formula for the volume of a cube.(1 point)
Responses
437,400 in.3
437,400 in. cubed
1,350 in.3
1,350 in. cubed
5,832 in.3
5,832 in. cubed
24,300 in.2
24,300 in. squared
Responses
437,400 in.3
437,400 in. cubed
1,350 in.3
1,350 in. cubed
5,832 in.3
5,832 in. cubed
24,300 in.2
24,300 in. squared
Answers
GPT-4o mini
To calculate the space needed to transport 75 boxes, we first need to find the volume of a single box and then multiply by the number of boxes.
The formula for the volume \( V \) of a cube is given by:
\[
V = s^3
\]
where \( s \) is the side length of the cube.
For this problem:
1. The side length \( s \) is 18 inches.
2. Calculate the volume of one box:
\[
V = 18^3 = 18 \times 18 \times 18
\]
Calculating step-by-step:
\[
18 \times 18 = 324
\]
\[
324 \times 18 = 5,832 \, \text{in}^3
\]
So, the volume of one box is \( 5,832 \, \text{in}^3 \).
3. Now, to find the total volume for 75 boxes:
\[
\text{Total Volume} = 75 \times 5,832 \, \text{in}^3
\]
Calculating this gives:
\[
75 \times 5,832 = 437,400 \, \text{in}^3
\]
So, the total space needed to transport the boxes is:
**437,400 in.³**
The formula for the volume \( V \) of a cube is given by:
\[
V = s^3
\]
where \( s \) is the side length of the cube.
For this problem:
1. The side length \( s \) is 18 inches.
2. Calculate the volume of one box:
\[
V = 18^3 = 18 \times 18 \times 18
\]
Calculating step-by-step:
\[
18 \times 18 = 324
\]
\[
324 \times 18 = 5,832 \, \text{in}^3
\]
So, the volume of one box is \( 5,832 \, \text{in}^3 \).
3. Now, to find the total volume for 75 boxes:
\[
\text{Total Volume} = 75 \times 5,832 \, \text{in}^3
\]
Calculating this gives:
\[
75 \times 5,832 = 437,400 \, \text{in}^3
\]
So, the total space needed to transport the boxes is:
**437,400 in.³**