A rectangular pyramid has a length of 7cm and a width of 9cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work
The formula for the volume of a pyramid is V = (1/3) * B * h, where B is the base area and h is the height.
The base area of a rectangular pyramid is given by B = length * width.
Given:
Length = 7cm
Width = 9cm
Volume = 231 cubic centimeters
Substituting the given values into the formula, we have:
231 = (1/3) * (7 * 9) * h
Simplifying, we have:
231 = (1/3) * 63 * h
Multiplying both sides by 3 to isolate h, we have:
693 = 63 * h
Dividing both sides by 63, we have:
h = 693 / 63
Simplifying, we have:
h = 11
Therefore, the height of the pyramid is 11cm.