Question

the volume of the rectangular pyramid is 320 cubic yards. the height, h, is 12 yards, and the length of the base, l, is 10 yards. what is the width of the base, w, of the rectangular pyramid? (not drawn to scale) a 11 yd b 4 yd c 8 yd d 24 yd

Explanation:

Step1: Recall the volume formula for a rectangular pyramid

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 the given values into the formula

We know that \(V = 320\) cubic yards, \(h=12\) yards, and \(l = 10\) yards. Substituting these into the formula \(320=\frac{1}{3}\times10\times w\times12\).
First, simplify the right - hand side: \(\frac{1}{3}\times10\times12\times w=( \frac{1}{3}\times12)\times10\times w = 4\times10\times w=40w\).
So the equation becomes \(320 = 40w\).

Step3: Solve for \(w\)

To solve for \(w\), divide both sides of the equation \(320 = 40w\) by \(40\). We get \(w=\frac{320}{40}\).
\(w = 8\) yards.

Answer:

C. 8 yd