To find the height of a solid right pyramid with a square base, let's start with the formula for the volume of such a pyramid. The volume [tex]\( V \)[/tex] of a pyramid can be calculated using the following formula:
[tex]\[ V = \frac{1}{3} \times \text{base\_area} \times \text{height} \][/tex]
For a pyramid with a square base, the base area can be given by the square of the side length [tex]\( y \)[/tex]:
[tex]\[ \text{base\_area} = y^2 \][/tex]
Substituting the base area into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times y^2 \times \text{height} \][/tex]
Now, we need to isolate the height on one side of this equation. To do this, follow these steps:
1. Multiply both sides of the equation by 3 to eliminate the fraction:
[tex]\[ 3V = y^2 \times \text{height} \][/tex]
2. Divide both sides of the equation by [tex]\( y^2 \)[/tex] to solve for the height:
[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] units
This shows that the correct expression for the height of the pyramid is [tex]\(\frac{3V}{y^2}\)[/tex] units.
