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Base Radius of Truncated Cone Formula:
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The Base Radius of a Truncated Cone is the distance from the center to any point on the circumference of the larger circular base of the truncated cone. It's a fundamental geometric measurement used in various engineering and architectural applications.
The calculator uses the geometric formula:
Where:
Explanation: This formula derives from the Pythagorean theorem applied to the right triangle formed by the height, slant height, and the difference between base and top radii.
Details: Accurate calculation of the base radius is crucial for determining the volume, surface area, and other geometric properties of truncated cones. It's essential in construction, manufacturing, and various engineering applications where conical frustums are used.
Tips: Enter top radius, slant height, and height in meters. All values must be positive, and slant height must be greater than the height. The calculator will compute the base radius using the geometric formula.
Q1: What is a truncated cone?
A: A truncated cone (or conical frustum) is a cone with the tip cut off by a plane parallel to the base, resulting in two parallel circular faces of different sizes.
Q2: Why is the slant height important in this calculation?
A: The slant height connects the edges of the top and base circles, forming the hypotenuse of the right triangle needed for the Pythagorean calculation.
Q3: What units should I use for the inputs?
A: The calculator uses meters, but you can use any consistent unit of length as long as all measurements are in the same unit.
Q4: What if the slant height is less than the height?
A: This is geometrically impossible for a truncated cone. The slant height must always be greater than the perpendicular height.
Q5: Can this formula be used for complete cones?
A: Yes, for a complete cone, the top radius would be 0, and the formula simplifies to \( r_{Base} = \sqrt{h_{Slant}^2 - h^2} \).