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 5,832 in.3 5,832 in. cubed 437,400 in.3 437,400 in. cubed 1,350 in.3 1,350 in. cubed 24,300 in.2
Answers
GPT-4o mini
To determine how much space the truck service needs to transport the 75 boxes, we first need to calculate the volume of a single box and then multiply that 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.
Given that the side length \( s \) of each box is 18 inches, we can calculate the volume of one box:
\[
V = 18^3 = 18 \times 18 \times 18
\]
Calculating this step by step:
1. \( 18 \times 18 = 324 \)
2. \( 324 \times 18 = 5,832 \)
Thus, the volume of one box is \( 5,832 \, \text{in}^3 \).
Now, to find the total volume for 75 boxes, we multiply the volume of one box by the number of boxes:
\[
\text{Total Volume} = 75 \times 5,832
\]
Calculating this:
1. \( 75 \times 5,832 = 437,400 \, \text{in}^3 \)
Thus, the total space needed to transport the 75 boxes is \( 437,400 \, \text{in}^3 \).
The correct response is:
**437,400 in. cubed**.
The formula for the volume \( V \) of a cube is given by:
\[
V = s^3
\]
where \( s \) is the side length of the cube.
Given that the side length \( s \) of each box is 18 inches, we can calculate the volume of one box:
\[
V = 18^3 = 18 \times 18 \times 18
\]
Calculating this step by step:
1. \( 18 \times 18 = 324 \)
2. \( 324 \times 18 = 5,832 \)
Thus, the volume of one box is \( 5,832 \, \text{in}^3 \).
Now, to find the total volume for 75 boxes, we multiply the volume of one box by the number of boxes:
\[
\text{Total Volume} = 75 \times 5,832
\]
Calculating this:
1. \( 75 \times 5,832 = 437,400 \, \text{in}^3 \)
Thus, the total space needed to transport the 75 boxes is \( 437,400 \, \text{in}^3 \).
The correct response is:
**437,400 in. cubed**.