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

Answer 1

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**