To find the height of a square pyramid, we can use the formula for the volume of a pyramid, which is given by:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height.
In this case, the volume V is 8 cubic feet. Since we have a square pyramid, the base is a square, and the area B can be calculated by squaring the length of one side of the base.
Let’s analyze the base lengths given: 2 feet, 6 feet, 16 feet, 12 feet, and 4 feet. Among these, we need to determine which one represents the base length of the pyramid.
For this example, let’s consider a base length of 4 feet. Then, the area of the base would be:
B = side length² = 4² = 16 square feet.
Now we can substitute this into the volume formula:
8 = (1/3) * 16 * h
To isolate h, we can first multiply both sides by 3:
24 = 16 * h
Next, divide both sides by 16:
h = 24 / 16 = 1.5 feet.
So, the height of the square pyramid with a base length of 4 feet and a volume of 8 cubic feet is 1.5 feet.