Question

the volume of a solid right pyramid with a square base is v units³ and the length of the base edge is y units. which expression represents the height of the pyramid?
○ \\(\frac{3v}{y^2}\\)units
○ \\((3v - y^2)\\)units
○ \\((v - 3y^2)\\)units
○ \\(\frac{v}{3y^2}\\)units

Explanation:

Step1: Recall the volume formula for a square - based pyramid

The volume \( V \) of a right pyramid with a square base is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid. For a square base with side length \( y \), the area of the base \( B = y\times y=y^{2}\). So the volume formula becomes \( V=\frac{1}{3}y^{2}h \), where \( h \) is the height of the pyramid.

Step2: Solve the formula for \( h \)

We start with the equation \( V = \frac{1}{3}y^{2}h \). To isolate \( h \), we first multiply both sides of the equation by \( 3 \) to get rid of the fraction on the right - hand side.
\( 3V=y^{2}h \)
Then, we divide both sides of the equation by \( y^{2} \) (assuming \( y
eq0 \)) to solve for \( h \).
\( h=\frac{3V}{y^{2}} \)

Answer:

\(\frac{3V}{y^{2}}\) units (corresponding to the first option)