Question

the formula for the volume of a pyramid is $v=\frac{1}{3}bh$, where $v$ is the volume, $b$ is the area of the base, and $h$ is the height. what is the height of a pyramid if the area of the base is 27 square units and the volume is 54 cubic units?

Explanation:

Step1: Substitute given values

Given $V = 54$, $B=27$ into $V=\frac{1}{3}Bh$. So $54=\frac{1}{3}\times27\times h$.

Step2: Solve for h

First simplify right - hand side: $\frac{1}{3}\times27 = 9$. Then $54 = 9h$. Divide both sides by 9, $h=\frac{54}{9}=6$.

Answer:

6