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 of your work.

Answer 1

The formula for the volume of a pyramid is given by:

V = (1/3) * base area * height

In this case, the base area is the area of the rectangle, which is given by:

A = length * width
A = 7cm * 9cm
A = 63cm^2

We know that V = 231cm^3, so we can rearrange the formula to solve for the height:

V = (1/3) * A * h
231cm^3 = (1/3) * 63cm^2 * h

Multiplying both sides by 3:

693cm^3 = 63cm^2 * h

Dividing both sides by 63cm^2:

h = 693cm^3 / 63cm^2
h = 11cm

Therefore, the height of the rectangular pyramid is 11cm.