Question
If the volume of a right rectangular prism is 1.5 in to the third and it's length and width have a product of 1.5 in squared what is the height of the prism
Answers
GPT-4o mini
To solve for the height of the right rectangular prism, we start with the formula for the volume of a right rectangular prism, which is:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
Given:
1. The volume \( V = 1.5 \) cubic inches.
2. The product of the length and width \( l \times w = 1.5 \) square inches.
Let \( h \) be the height of the prism. We can express the volume as follows:
\[
V = l \times w \times h
\]
Substituting the given values:
\[
1.5 = (l \times w) \times h
\]
Since \( l \times w = 1.5 \), we substitute this into the volume equation:
\[
1.5 = 1.5 \times h
\]
Now, to solve for \( h \), divide both sides by \( 1.5 \):
\[
h = \frac{1.5}{1.5} = 1
\]
Thus, the height of the prism is:
\[
\boxed{1} \text{ inch}
\]
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
Given:
1. The volume \( V = 1.5 \) cubic inches.
2. The product of the length and width \( l \times w = 1.5 \) square inches.
Let \( h \) be the height of the prism. We can express the volume as follows:
\[
V = l \times w \times h
\]
Substituting the given values:
\[
1.5 = (l \times w) \times h
\]
Since \( l \times w = 1.5 \), we substitute this into the volume equation:
\[
1.5 = 1.5 \times h
\]
Now, to solve for \( h \), divide both sides by \( 1.5 \):
\[
h = \frac{1.5}{1.5} = 1
\]
Thus, the height of the prism is:
\[
\boxed{1} \text{ inch}
\]