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:
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Substitute the known values into the volume formula:
- Correct: \( 225 = (7.5) (w) (5) \)
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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.)
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The width of the prism is 6 m.
- Incorrect: We haven't calculated the width yet.
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The width of the prism is 5.5 m.
- Incorrect: Again, we haven't calculated the width yet.
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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 \( w \).
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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:
- \( 225 = (7.5) (w) (5) \)
- 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:
- Calculate \( 7.5 \times 5 = 37.5 \).
- The equation now reads \( 225 = 37.5w \).
- 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.
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