Question
the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2 , what is the height of this prism?(1 point)
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Answers
GPT-4o mini
To find the height of the right rectangular prism, we can use the formula for the volume of a rectangular prism, which is:
\[
V = l \times w \times h
\]
Where:
- \(V\) is the volume,
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height.
According to the problem, we have the following information:
- Volume \(V = 1.5 \, \text{in}^3\)
- The product of the length and width \(l \times w = 1.5 \, \text{in}^2\)
Now, we can express the height \(h\) in terms of the volume and the product of length and width:
\[
h = \frac{V}{l \times w}
\]
Substituting the provided values into the equation:
\[
h = \frac{1.5 \, \text{in}^3}{1.5 \, \text{in}^2}
\]
Calculating this:
\[
h = 1 \, \text{in}
\]
Thus, the height of the prism is:
\[
\boxed{1 \, \text{in}}
\]
\[
V = l \times w \times h
\]
Where:
- \(V\) is the volume,
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height.
According to the problem, we have the following information:
- Volume \(V = 1.5 \, \text{in}^3\)
- The product of the length and width \(l \times w = 1.5 \, \text{in}^2\)
Now, we can express the height \(h\) in terms of the volume and the product of length and width:
\[
h = \frac{V}{l \times w}
\]
Substituting the provided values into the equation:
\[
h = \frac{1.5 \, \text{in}^3}{1.5 \, \text{in}^2}
\]
Calculating this:
\[
h = 1 \, \text{in}
\]
Thus, the height of the prism is:
\[
\boxed{1 \, \text{in}}
\]