Question

Use the formula for the volume of a right rectangular prism to calculate the volume of a box with dimensions 5 ft.× 2 yd.×16 in.
5

ft
.
×

2
yd.
×
16

in
.
.(1 point)
Responses

160 in.3
160

in
.
3
160 in cubed

160 ft.3
160

ft.
3
160 ft cubed

69,120 ft.3
69
,
120

ft.
3
69,120 ft cubed

69,120 in.3

Answer 1

To calculate the volume of a rectangular prism, we use the formula:

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

First, we need to convert all measurements to the same unit. Let's convert everything to inches.

1. **Convert feet to inches:**
- \(5 \, \text{ft} = 5 \times 12 \, \text{in} = 60 \, \text{in}\)

2. **Convert yards to inches:**
- \(2 \, \text{yd} = 2 \times 36 \, \text{in} = 72 \, \text{in}\)

3. **The height is already in inches:**
- \(16 \, \text{in}\)

Now we have the dimensions in inches:
- Length: \(60 \, \text{in}\)
- Width: \(72 \, \text{in}\)
- Height: \(16 \, \text{in}\)

Now we can calculate the volume:

\[
\text{Volume} = 60 \, \text{in} \times 72 \, \text{in} \times 16 \, \text{in}
\]

Calculating step-by-step:

\[
60 \times 72 = 4320 \, \text{in}^2
\]

Now, multiply by the height:

\[
4320 \times 16 = 69120 \, \text{in}^3
\]

Therefore, the volume of the box is:

\[
\boxed{69,120 \, \text{in}^3}
\]