To find the volume of a right circular cone, one should use the formula pi * r^{2} * h / 3. This is known as Cavalieri's Principle. In this formula, the value for "r" is the radius of the base of the cone and "h" is the height.
Continue ReadingCavalieri's Principle is named after Italian mathematician Bonaventura Cavalieri, who made specific contributions to the development of integral calculus. Another name for the principle is the Method of Indivisibles, and it applies to both 2-dimensional and 3-dimensional objects. In general, the principle is a method to find the volume of any solid, regardless of its shape, when its cross-sections by parallel planes have equivalent areas.
For example, a cone with a radius of 5 and a height of 6 has a volume of approximately 157.08. To solve this problem, insert the numbers for the values in Cavalieri's Principle: 3.1416 * 5^{2} * 6 / 3. This simplifies to 3.1416 * 25 * 2, or approximately 157.08. Since the number pi is infinite, it is rounded for the purpose of this formula to 3.1416. The more digits it rounds to, the more specific the final answer will be. However, the final answer should always use an approximate rather than a true equal sign.
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