Let's consider the problem of finding the height of a right pyramid with a square base, given the volume and the length of the base edge.
### Step-by-Step Solution:
1. Volume Formula for a Pyramid:
The volume [tex]\( V \)[/tex] of a right pyramid with a square base is given by:
[tex]\[
V = \frac{1}{3} \times \text{base\_area} \times \text{height}
\][/tex]
2. Area of the Square Base:
Since the base is a square with edge length [tex]\( y \)[/tex], the area of the base ([tex]\(\text{base\_area}\)[/tex]) is:
[tex]\[
\text{base\_area} = y^2
\][/tex]
3. Substitute Base Area into Volume Formula:
Substitute [tex]\( y^2 \)[/tex] for the base area in the volume formula:
[tex]\[
V = \frac{1}{3} \times y^2 \times \text{height}
\][/tex]
4. Solve for Height:
We need to solve for the height ([tex]\(\text{height}\)[/tex]). Rearrange the equation to isolate height on one side:
[tex]\[
\text{height} = \frac{3V}{y^2}
\][/tex]
Thus, the expression that represents the height of the pyramid is:
[tex]\[
\boxed{\frac{3V}{y^2}}
\][/tex]
So, among the given choices, the correct option is:
[tex]\[
\frac{3 V}{y^2} \text{ units}
\][/tex]
