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. Show all your work(
The formula for the volume of a pyramid is V = (1/3) * base_area * height, where base_area is the area of the base and height is the height of the pyramid.
In this case, the base of the pyramid is a rectangle with length 7 cm and width 9 cm, so the base_area = 7 cm * 9 cm = 63 cm^2.
Given that the volume of the pyramid is 231 cubic centimeters, we can now solve for the height.
231 = (1/3) * 63 cm^2 * height
Multiplying both sides of the equation by 3 to get rid of the fraction:
693 = 63 cm^2 * height
Dividing both sides of the equation by 63 cm^2:
height = 693 / 63 = 11 cm
Therefore, the height of the pyramid is 11 cm.