Question

The dimensions of a rectangular shipping crate are 2.5 ft., 2.5 ft., and 4 ft. If there were a similar shipping crate with a scale factor of 3, what would be the volume of the new shipping crate?(1 point)
Responses

225 ft.3
225 ft. cubed

675 ft.3
675 ft. cubed

75 ft.3
75 ft. cubed

25 ft.3

Answer 1

To find the volume of the original shipping crate, we use the formula for the volume of a rectangular prism:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

The dimensions of the original crate are:
- Length = 2.5 ft
- Width = 2.5 ft
- Height = 4 ft

Calculating the volume:

\[
\text{Volume} = 2.5 \, \text{ft} \times 2.5 \, \text{ft} \times 4 \, \text{ft} = 25 \, \text{ft}^3
\]

If there is a new shipping crate with a scale factor of 3, the dimensions of the new crate would be 3 times the original dimensions:

- New length = \(3 \times 2.5 \, \text{ft} = 7.5 \, \text{ft}\)
- New width = \(3 \times 2.5 \, \text{ft} = 7.5 \, \text{ft}\)
- New height = \(3 \times 4 \, \text{ft} = 12 \, \text{ft}\)

Now we calculate the volume of the new shipping crate:

\[
\text{New Volume} = 7.5 \, \text{ft} \times 7.5 \, \text{ft} \times 12 \, \text{ft}
\]

Calculating this step-by-step:

1. \(7.5 \times 7.5 = 56.25\)
2. \(56.25 \times 12 = 675\)

Thus, the volume of the new shipping crate is \(675 \, \text{ft}^3\).

The correct response is:

**675 ft.³**