the volume of the rectangular pyramid is 360 cubic feet. the height, h, is 15 feet, and the width of the…

the volume of the rectangular pyramid is 360 cubic feet. the height, h, is 15 feet, and the width of the base, w, is 6 feet. what is the length of the base, l, of the rectangular pyramid? (not drawn to scale) a 12 ft b 13 ft c 36 ft d 90 ft

the volume of the rectangular pyramid is 360 cubic feet. the height, h, is 15 feet, and the width of the base, w, is 6 feet. what is the length of the base, l, of the rectangular pyramid? (not drawn to scale) a 12 ft b 13 ft c 36 ft d 90 ft

Answer

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - pyramid is $V=\frac{1}{3}lwh$, where $V$ is the volume, $l$ is the length of the base, $w$ is the width of the base, and $h$ is the height.

Step2: Substitute given values

We know that $V = 360$ cubic feet, $h=15$ feet, and $w = 6$ feet. Substituting these values into the formula gives $360=\frac{1}{3}\times l\times6\times15$.

Step3: Simplify the right - hand side

First, simplify $\frac{1}{3}\times6\times15$. $\frac{1}{3}\times6\times15 = 30$. So the equation becomes $360 = 30l$.

Step4: Solve for $l$

Divide both sides of the equation $360 = 30l$ by 30. We get $l=\frac{360}{30}=12$.

Answer:

A. 12 ft