Question

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

Explanation:

Step1: Recall the volume formula for a pyramid

The volume formula for a pyramid is \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height. For a rectangular pyramid, the base is a rectangle, so \( B = lw \) (where \( l \) is the length, \( w \) is the width of the base). Thus, the volume formula becomes \( V=\frac{1}{3}lwh \).

Step2: Substitute the known values into the formula

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

Step3: Simplify the right - hand side of the equation

First, calculate \( \frac{1}{3}\times6\times15 \). \( \frac{1}{3}\times6 = 2 \), and then \( 2\times15=30 \). So the equation becomes \( 360 = 30l \).

Step4: Solve for \( l \)

To find \( l \), divide both sides of the equation \( 360 = 30l \) by 30. \( l=\frac{360}{30}=12 \) feet.

Answer:

A. 12 ft