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
24,300 in.2
24,300 in. squared
5,832 in.3
5,832 in. cubed
1,350 in.3
1,350 in. cubed
437,400 in.3
437,400 in. cubed
Responses
24,300 in.2
24,300 in. squared
5,832 in.3
5,832 in. cubed
1,350 in.3
1,350 in. cubed
437,400 in.3
437,400 in. cubed
Answers
GPT-4o mini
To find the total space needed to transport the 75 boxes, we first need to calculate the volume of a single box using the formula for the volume of a cube, which is:
\[ V = s^3 \]
where \( s \) is the side length of the cube.
Given that the side length \( s \) is 18 inches:
\[ V = 18^3 = 18 \times 18 \times 18 \]
Calculating this step by step:
1. \( 18 \times 18 = 324 \)
2. \( 324 \times 18 = 5,832 \) cubic inches
So, the volume of one box is \( 5,832 \) in³.
Next, to find the total volume for 75 boxes:
\[ \text{Total Volume} = 75 \times 5,832 \]
Calculating that:
\[ 75 \times 5,832 = 437,400 \] cubic inches
Therefore, the total space needed to transport the boxes is:
**437,400 in³** (437,400 in. cubed).
\[ V = s^3 \]
where \( s \) is the side length of the cube.
Given that the side length \( s \) is 18 inches:
\[ V = 18^3 = 18 \times 18 \times 18 \]
Calculating this step by step:
1. \( 18 \times 18 = 324 \)
2. \( 324 \times 18 = 5,832 \) cubic inches
So, the volume of one box is \( 5,832 \) in³.
Next, to find the total volume for 75 boxes:
\[ \text{Total Volume} = 75 \times 5,832 \]
Calculating that:
\[ 75 \times 5,832 = 437,400 \] cubic inches
Therefore, the total space needed to transport the boxes is:
**437,400 in³** (437,400 in. cubed).