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

1 answer

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 \( 5,832 , \text{in}^3 \).

  1. 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