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How is the volume of an ellipsoid calculated?

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To determine the volume of an ellipsoid, the object's length must first be multiplied by its width and then by its height, followed by a final multiplication by a constant which is equal to the value of pi divided by 6. Using the 5-decimal-place value of pi, 3.14159, and dividing by 6, a value of 0.523598 is obtained for the constant and final multiplier. Thus, the volume of an ellipsoid with a length of 10 inches, width of 10 inches and height of 5 inches is determined by 10 x 10 x 5 x 0.523598, which equals 261.799 cubic inches.

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An ellipsoid is a three-dimensional version of an ellipse in the same manner as a sphere is a three-dimensional version of a circle. It is uncertain when the concept of an ellipse was discovered, though it is believed that the ancient Greeks knew around 350 B.C. that slicing a section of a cone by a two-dimensional plane at an angle, rather than parallel to its base, would produce the conic geometric shape known as an ellipse.

Rather than being a perfect sphere, the Earth is an ellipsoid. Isaac Newton and other British scientists were the first to theorize that the Earth was an ellipsoid. Measurements taken at the equator and at the Arctic Circle by a French survey expedition in 1753 proved the theory to be correct.

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