Sara correctly found the volume of the square pyramid to be 1980 ft3 . What is the height of the pyramid? Click HERE for the Formula Reference Sheet.
To find the height of the square pyramid, use the formula:
V = (1/3) * b^2 * h
where V is the volume of the pyramid, b is the length of the base of the pyramid, and h is the height of the pyramid.
Given that V = 1980 ft3, and the base of the pyramid is a square, so b^2 is the same as the area of the base. Let's denote b as the length of one side of the square base.
1980 = (1/3) * b^2 * h
Multiplying both sides by 3 to remove the fraction gives:
5940 = b^2 * h
Since the base of the pyramid is a square, the area of the base is b^2. Therefore, to find b, we need to find the square root of the area of the base.
b^2 = 5940
b = √5940
b ≈ 77.12 ft
Now, substitute the value of b back into the formula to solve for h:
1980 = (1/3) * 77.12^2 * h
1980 = (1/3) * 5944.38 * h
1980 = 1981.46h
h ≈ 1 ft
Therefore, the height of the square pyramid is approximately 1 ft.