Question
If 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?
3 and its length and width have a product of
1.5 in.
2
, what is the height of this prism?
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 given by:
\[
V = l \times w \times h
\]
where \( V \) is the volume, \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- The volume \( V = 1.5 \, \text{in}^3 \)
- The product of length and width \( l \times w = 1.5 \, \text{in}^2 \)
We can substitute the product of length and width into the volume formula:
\[
V = (l \times w) \times h
\]
Substituting the known values, we have:
\[
1.5 \, \text{in}^3 = 1.5 \, \text{in}^2 \times h
\]
To solve for the height \( h \), we divide both sides by \( 1.5 \, \text{in}^2 \):
\[
h = \frac{1.5 \, \text{in}^3}{1.5 \, \text{in}^2}
\]
Calculating the right side:
\[
h = 1 \, \text{in}
\]
Hence, 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, and \( h \) is the height.
Given:
- The volume \( V = 1.5 \, \text{in}^3 \)
- The product of length and width \( l \times w = 1.5 \, \text{in}^2 \)
We can substitute the product of length and width into the volume formula:
\[
V = (l \times w) \times h
\]
Substituting the known values, we have:
\[
1.5 \, \text{in}^3 = 1.5 \, \text{in}^2 \times h
\]
To solve for the height \( h \), we divide both sides by \( 1.5 \, \text{in}^2 \):
\[
h = \frac{1.5 \, \text{in}^3}{1.5 \, \text{in}^2}
\]
Calculating the right side:
\[
h = 1 \, \text{in}
\]
Hence, the height of the prism is:
\[
\boxed{1 \, \text{in}}
\]