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 rectangular pyramid is given by:
Volume = (1/3) * Base Area * Height
We are given that the length of the rectangular pyramid is 7 cm and the width is 9 cm. The volume is given as 231 cubic centimeters.
We can start by finding the base area of the pyramid:
Base Area = length * width
Base Area = 7 cm * 9 cm = 63 cm^2
Now we can substitute the values into the formula for the volume of the pyramid:
231 cm^3 = (1/3) * 63 cm^2 * Height
To solve for the height, we rearrange the equation:
Height = (3 * 231 cm^3) / (63 cm^2)
Height = (693 cm^3) / (63 cm^2)
Height = 11 cm
Therefore, the height of the rectangular pyramid is 11 cm.