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)

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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid. The volume of a pyramid is given by the formula V = (1/3) * base area * height. In this case, the volume is given as 231 cubic centimeters.

First, let's find the base area of the pyramid. The base of the rectangular pyramid is a rectangle with a length of 7 cm and a width of 9 cm. The formula to find the area of a rectangle is A = length * width. So, the base area of the pyramid is 7 cm * 9 cm, which is equal to 63 square cm.

Now, let's substitute the values into the formula for the volume of a pyramid. We have 231 cubic cm = (1/3) * 63 square cm * height.

To solve for the height, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 3 first, to cancel out the (1/3) coefficient.

3 * 231 cubic cm = 3 * (1/3) * 63 square cm * height.

693 cubic cm = 63 square cm * height.

Now we divide both sides of the equation by 63 square cm to solve for the height.

Height = 693 cubic cm / 63 square cm.

Height = 11 cm.

So, the height of the rectangular pyramid is 11 cm.