To find the height of a square pyramid when you know its volume and the length of its base, you can use the formula for the volume of a pyramid:
Volume = (1/3) × base area × height
For a square pyramid, the base area can be calculated as:
Base Area = base length × base length
In this case, the base length is 4 feet, so the base area is:
Base Area = 4 ft × 4 ft = 16 square feet
Now we can plug the values into the volume formula. We know the volume is 32 cubic feet:
32 = (1/3) × 16 × height
To isolate the height, first multiply both sides of the equation by 3:
96 = 16 × height
Next, divide both sides by 16:
height = 96 / 16 = 6 feet
Thus, the height of the pyramid is 6 feet.