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 - y²) units (v - 3y²) units $\frac{v}{3y^{2}}$ units

Explanation:

Step1: Recall volume formula

The volume formula for a square - based pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height. The base is a square with side - length $y$, so the base area $B = y^{2}$.

Step2: Solve for height

We have $V=\frac{1}{3}y^{2}h$. Multiply both sides of the equation by $3$ to get $3V=y^{2}h$. Then divide both sides by $y^{2}$ to isolate $h$. So, $h = \frac{3V}{y^{2}}$.

Answer:

$\frac{3V}{y^{2}}$ units