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)

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

GPT-4o mini · Answer

To find the space needed to transport the 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:

$V = s^{3}$

where $s$ is the side length of the cube.

Given that the side length $s$ is 18 inches, we calculate the volume of one box:

$V = 18^{3} = 18 \times 18 \times 18$

Calculating this step-by-step:

$18 \times 18 = 324$
$324 \times 18 = 5, 832$ cubic inches

Now that we have the volume of one box, we need to calculate the total volume required for 75 boxes:

$Total Volume = 75 \times 5, 832$

Calculating this:

$75 \times 5, 832 = 437, 400 cubic inches$

So, the service will need a total space of 437,400 cubic inches to transport the boxes.

The correct response is:

437,400 in. cubed