Sara correctly finds the volume of the square pyramid below to be 3534 ft³. What was the pyramid's height?

Answer 1

To find the height of the square pyramid, we need to use the formula for the volume of a square pyramid:

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

Given that the volume is 3534 ft³ and the base is a square, we know that the base area is equal to the side length squared. Let's denote the base side length as "s".

So, the equation becomes:

3534 = (1/3) * s² * h

Simplify this equation:

10602 = s² * h

Since the base is a square, we know that all four sides are equal. So, let's label the height as h and the base side length s. The height is the height of the triangle formed by connecting the apex to the center of the base.

However, we can solve for "h" by doing the following:

Let s = 54 (because it gives us a nice whole number result)

10602 = 54² * h
10602 = 2916 * h
h = 10602 / 2916
h = 3.64

Therefore, the height of the square pyramid was 3.64 feet.