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Height Formula:
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The Slant Height to Height calculation determines the vertical height of a cone or pyramid using the slant height and base radius. This calculation is based on the Pythagorean theorem applied to the right triangle formed by the height, radius, and slant height.
The calculator uses the Pythagorean theorem:
Where:
Explanation: The slant height, height, and radius form a right triangle where the slant height is the hypotenuse, making this a direct application of the Pythagorean theorem.
Details: Accurate height calculation is essential for determining volume, surface area, and other geometric properties of cones and pyramids. It's crucial in architecture, engineering, and manufacturing applications.
Tips: Enter slant height and radius in consistent units. Ensure slant height is greater than radius for valid results. All values must be positive numbers.
Q1: What is the difference between height and slant height?
A: Height is the perpendicular distance from apex to base, while slant height is the diagonal distance from apex to edge of base along the surface.
Q2: Can this formula be used for pyramids?
A: Yes, this formula works for right circular cones and regular pyramids where the apex is directly above the center of the base.
Q3: What if the slant height equals the radius?
A: If slant height equals radius, the height would be zero, which is geometrically impossible for a cone or pyramid.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric shapes. Real-world applications may require adjustments for manufacturing tolerances.
Q5: What units should I use?
A: Use consistent units (cm, m, inches, etc.) for both measurements. The result will be in the same units.