Right Rectangular Prisms & Pyramids Unit Test

Question

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. (2 points)

Answer 1

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

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

In this case, the base of the pyramid is a rectangle with a length of 7 cm and a width of 9 cm.

The base area can be calculated as:

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. Substituting the values into the formula, we have:

231 cm^3 = (1/3) * 63 cm^2 * height

To find 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

Simplifying the expression on the left side:

231 cm^3 / (1/3) * 63 cm^2 = height
231 cm^3 / (1/3) * 63 cm^2 = height
231 cm^3 / (21/3) cm^2 = height
231 cm^3 / 21/3 cm^2 = height
f(j)
69 cm = height

Therefore, the height of the rectangular pyramid is 69 cm.