A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its value is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work
To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid which is given by:
Volume = (1/3) * base area * height
We are given the length and width of the pyramid, so we can find the base area using:
Base area = length * width
Base area = 7 cm * 9 cm
Base area = 63 cm^2
Now we can plug in the values into the formula to find the height:
231 cm^3 = (1/3) * 63 cm^2 * height
Multiplying both sides by 3 gives:
3 * 231 cm^3 = 63 cm^2 * height
693 cm^3 = 63 cm^2 * height
Dividing by 63 cm^2 gives:
height = 693 cm^3 / 63 cm^2
height = 11 cm
Therefore, the height of the pyramid is 11 cm.