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Frustum Volume Formula:
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A frustum of a cone is the portion of a cone that lies between two parallel planes cutting it. It's a common shape in everyday objects like buckets, lampshades, and certain drinking glasses.
The calculator uses the frustum volume formula:
Where:
Explanation: The formula accounts for the combined area of the three surfaces (bottom, top, and the lateral side) multiplied by the height and the 1/3 coefficient characteristic of cone-related volumes.
Details: Frustum volume calculations are used in engineering (tank design), architecture (structural elements), manufacturing (mold design), and even in culinary measurements for cooking vessels.
Tips: Enter all dimensions in the same units. Ensure the larger radius corresponds to the wider base of the frustum. All values must be positive numbers.
Q1: What if my frustum isn't from a cone?
A: This formula specifically applies to conical frustums. Other frustum shapes (like pyramidal frustums) have different volume formulas.
Q2: How accurate is the calculation?
A: The calculation is mathematically exact for perfect frustums. Real-world accuracy depends on how precisely your measurements match an ideal frustum shape.
Q3: Can I use this for tapered cylinders?
A: Yes, a tapered cylinder is essentially a conical frustum, so this formula applies.
Q4: What if my smaller radius is larger than my larger radius?
A: The calculator will still work, but your "frustum" would actually be an inverted frustum. Ensure you've assigned the radii correctly.
Q5: How does this relate to the full cone volume formula?
A: If r = 0, the formula reduces to the standard cone volume formula (V = ⅓πR²h). If r = R, it becomes the cylinder formula (V = πR²h).