Question

A rectangular prism has a length of 7.5 m, a height of 5 m, and a volume of 225 m3.

A prism has a length of 7.5 meters, width of w, and height of 5 meters.

Which steps are correct to find the width of the prism? Check all that apply.
Substitute the known values into the volume formula.
225 = (7.5) (w) (5)
Substitute the known values into the volume formula.
7.5 = (225) (w) (5)
The width of the prism is 6 m.
The width of the prism is 5.5 m.
Divide StartFraction 225 Over 37.5 EndFractionto find the width.
Divide StartFraction 225 Over 12.5 EndFractionto find the width.

Answer 1

To find the width of the prism, we can use the formula for the volume \( V \) of a rectangular prism, which is given by:

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

Given that the length is 7.5 m, the height is 5 m, and the volume is 225 m³, we can substitute these values into the formula. Here are the steps to identify which are correct:

1. **Substitute the known values into the volume formula:**
- **Correct:** \( 225 = (7.5) (w) (5) \)

2. **Substitute the known values into the volume formula:**
- **Incorrect:** \( 7.5 = (225) (w) (5) \) (The equation presented is not correct as it doesn't represent the volume formula.)

3. **The width of the prism is 6 m.**
- **Incorrect:** We haven't calculated the width yet.

4. **The width of the prism is 5.5 m.**
- **Incorrect:** Again, we haven't calculated the width yet.

5. **Divide \( \frac{225}{37.5} \) to find the width.**
- **Correct:** First, we can simplify the equation \( 225 = 37.5w \). \( 37.5 = 7.5 \times 5 \), so dividing \( 225 \) by \( 37.5 \) will give us \( w \).

6. **Divide \( \frac{225}{12.5} \) to find the width.**
- **Incorrect:** The correct divisor in this context is \( 37.5 \).

### Summary of Correct Steps
- Only the following steps are correct:
1. \( 225 = (7.5) (w) (5) \)
2. Divide \( \frac{225}{37.5} \) to find the width.

### Now, let's calculate the width:

From the equation \( 225 = (7.5)(w)(5) \), we can simplify it as follows:
1. Calculate \( 7.5 \times 5 = 37.5 \).
2. The equation now reads \( 225 = 37.5w \).
3. To find \( w \), divide both sides by \( 37.5 \):
\[
w = \frac{225}{37.5} = 6 \text{ m}
\]

So the correct width of the prism is 6 m.