Height Of Truncated Cone Given Slant Height Calculator

Formula Used:

\[ h = \sqrt{h_{Slant}^2 - (r_{Base} - r_{Top})^2} \]

Slant Height of Truncated Cone:

Base Radius of Truncated Cone:

Top Radius of Truncated Cone:

Height of Truncated Cone:

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1. What is the Height of Truncated Cone?

The height of a truncated cone is the vertical distance between the base and top circular surfaces. It is an important geometric measurement used in various engineering and architectural applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{h_{Slant}^2 - (r_{Base} - r_{Top})^2} \]

Where:

\( h \) — Height of Truncated Cone (m)
\( h_{Slant} \) — Slant Height of Truncated Cone (m)
\( r_{Base} \) — Base Radius of Truncated Cone (m)
\( r_{Top} \) — Top Radius of Truncated Cone (m)

Explanation: This formula applies the Pythagorean theorem to find the vertical height from the known slant height and the difference between base and top radii.

3. Importance of Height Calculation

Details: Calculating the height of a truncated cone is essential for determining volume, surface area, and other geometric properties. It's used in construction, manufacturing, and various engineering fields.

4. Using the Calculator

Tips: Enter slant height, base radius, and top radius in meters. All values must be positive numbers, and the slant height must be greater than the absolute difference between base and top radii.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cone?
A: A truncated cone is a cone with the apex cut off by a plane parallel to the base, resulting in two circular faces of different sizes.

Q2: Can this formula be used for any truncated cone?
A: Yes, this formula works for any right circular truncated cone where the cutting plane is parallel to the base.

Q3: What if the slant height is less than the radius difference?
A: The calculation would result in an imaginary number, indicating that such a truncated cone cannot exist with the given dimensions.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input measurements and a perfect geometric shape.

Q5: What are practical applications of this calculation?
A: This calculation is used in construction of conical structures, manufacturing of tapered components, and volume calculations for containers and storage vessels.