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:
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 base area can be calculated by multiplying the length and width:
Base area = length * width
Base area = 7 cm * 9 cm
Base area = 63 cm^2
We are also given that the volume of the pyramid is 231 cubic centimeters. Plugging in the given values into the formula:
231 cm^3 = (1/3) * 63 cm^2 * height
To solve for the height, we can isolate it by dividing both sides of the equation by (1/3) * 63 cm^2:
231 cm^3 / [(1/3) * 63 cm^2] = height
231 cm^3 / 21 cm^2 = height
Height = 11 cm
Therefore, the height of the rectangular pyramid is 11 cm.