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 pyramid volume formula

The volume of a square pyramid is given by $V = \frac{1}{3}Bh$, where $B$ is the area of the square base, and $h$ is the height.

Step2: Calculate base area

The base is a square with edge length $y$, so $B = y^2$. Substitute into the volume formula:
$V = \frac{1}{3}y^2h$

Step3: Solve for height $h$

Multiply both sides by 3: $3V = y^2h$
Divide both sides by $y^2$: $h = \frac{3V}{y^2}$

Answer:

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