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

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

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

5,832 in.3
5,832 in. cubed

24,300 in.2

1 answer

To determine the space needed to transport the boxes, we first calculate the volume of a single box using the formula for the volume of a cube:

\[ V = s^3 \]

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

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

\[ V = 18^3 = 18 \times 18 \times 18 \]

Calculating step by step:

  1. \( 18 \times 18 = 324 \)
  2. \( 324 \times 18 = 5,832 \)

So the volume of one box is \( 5,832 \) in³.

Next, we need to find the volume for 75 boxes:

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

Calculating that:

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

Thus, the total volume required to transport the 75 boxes is 437,400 in³.

The correct response is:

437,400 in.³