How to Calculate the Volume of Pyramids
You can calculate the volume of any pyramid with a single formula, regardless of the type of pyramid or how many sides it has. The volume of a pyramid is simply one-third the area of the base times the pyramid's height. The formula for the area of the base differs, of course, depending on how many sides it has, but once the area is calculated, the formula for volume remains the same.
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Instructions
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Calculate the area of the pyramid's base. Most pyramids have a square base, but some are triangular. Calculate the area of a square or rectangle by multiplying the length times the width. Calculate a triangle's area by multiplying the triangle's base times its height and dividing by two. The base and height of the triangle should not be confused with the base and height of the pyramid. For now, just find the area of the pyramid's base.
For example, for a square-based pyramid with a width and length of 10 feet each, the area would be 10 x 10 = 100 square feet.
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Measure the height of the pyramid. This is the actual height, and not the length of one side; if you drop a plumb-bob straight down from the pyramid's peak to the base, that would represent the distance you need to measure. To continue the example, say the height was also 10 feet.
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Use the formula volume equals one-third the area of the base times the height of the pyramid. In the example:
Volume = 1/3 x base area x height
Volume = 1/3 x 100 square feet x 10 feet
Volume = 333 cubic feet.
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- Photo Credit pyramid image by christine dedman from Fotolia.com
