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

437,400 in.3
437,400 in. cubed

1,350 in.3
1,350 in. cubed

5,832 in.3

Answer 1

To determine the space needed to transport the 75 boxes, we first need to calculate the volume of a single box. The formula for the volume of a cube is:

\[ V = s^3 \]

where \( s \) is the side length of the cube.

Given that the side length \( s \) of the boxes is 18 inches, we can calculate the volume of one box:

\[
V = 18^3
\]

Calculating \( 18^3 \):

\[
18 \times 18 = 324
\]
\[
324 \times 18 = 5,832 \, \text{in}^3
\]

So, the volume of one box is 5,832 cubic inches.

Now, to find the total volume for 75 boxes, we multiply the volume of one box by 75:

\[
\text{Total Volume} = 75 \times 5,832
\]

Calculating that:

\[
75 \times 5,832 = 437,400 \, \text{in}^3
\]

Therefore, the total space needed to transport the 75 boxes is **437,400 in.³**.