https://file.aiquickdraw.com/mathbot/file/1727393460126bosunwm0.jpg

To solve this, we need to recall the formula for the volume of a pyramid:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

Given that the pyramid has a square base with side length \( y \), the area of the base is:

\[
\text{Base Area} = y^2
\]

Therefore, the volume formula becomes:

\[
V = \frac{1}{3} \times y^2 \times h
\]

Now, solve for the height \( h \):

\[
h = \frac{3V}{y^2}
\]

Thus, the expression that represents the height of the pyramid is:

\[
\boxed{\frac{3V}{y^2}}
\]

This corresponds to the first option in the provided list.

Let me know if you would like further clarification, and here are five related questions to expand your understanding:

1. What is the general formula for the volume of a pyramid with any polygonal base?
2. How does the volume formula change for a cone?
3. If the length of the base edge \( y \) is doubled, how does the height change?
4. How would the formula for the height change if the pyramid had a triangular base?
5. What is the relationship between the slant height and the perpendicular height of a pyramid?

**Tip:** When solving for one variable in terms of others, always check for correct algebraic manipulation and units consistency.

The volume of a solid right pyramid with a square base is V units^3 and the length of the base edge is y units. Which expression represents the height of the pyramid?

Learn how to determine the height of a right pyramid with a square base when given the volume and base edge length. This solution uses the formula V = (1/3) * base area * height and solves for the height. Suitable for students in Grades 9-11.

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