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)

5 answers

The formula for the volume of a pyramid is:

Volume = 1/3 * base area * height

In this case, the base area is the area of the rectangular base, which is length * width. So, the base area is:

Base Area = 7 cm * 9 cm = 63 cm^2

We are given that the volume is 231 cubic centimeters. Plugging in the given values into the formula, we have:

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

Multiplying both sides of the equation by 3 to get rid of the fraction, we have:

231 cm^3 * 3 = 63 cm^2 * height

693 cm^3 = 63 cm^2 * height

Dividing both sides of the equation by 63 cm^2, we have:

693 cm^3 / 63 cm^2 = height

Simplifying the equation, we have:

11 cm = height

Therefore, the height of the pyramid is 11 cm.
Can you shorten your response?
To find the height of the pyramid, we can use the formula for the volume of a pyramid:

Volume = 1/3 * base area * height

Given that the length is 7 cm and the width is 9 cm, the base area is 7 cm * 9 cm = 63 cm^2.

We are also given that the volume is 231 cm^3.

Plugging in these values into the formula, we have:

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

Simplifying the equation, we find:

height = 11 cm

Therefore, the height of the pyramid is 11 cm.
Even smaller?
The rectangular pyramid has a height of 11 cm.