A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid, and please show all your work. (2 points)
The formula for the volume of a rectangular pyramid is V = (1/3) * l * w * h, where V is the volume, l is the length, w is the width, and h is the height.
Given:
l = 7 cm
w = 9 cm
V = 231 cubic cm
Using the formula, we can solve for h:
231 = (1/3) * 7 * 9 * h
First, simplify the right side of the equation:
231 = (7 * 9/3) * h
231 = (63/3) * h
231 = 21 * h
Next, divide both sides of the equation by 21 to isolate h:
h = 231/21
h = 11
Therefore, the height of the pyramid is 11 cm.