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 volume formula

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

Step2: Solve for height

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

Answer:

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