Height Of Frustum Of Cone Given Slant Height And Base Area Calculator

Formula Used:

\[ h = \sqrt{l^2 - \left( \sqrt{\frac{A_{Base}}{\pi}} - r \right)^2} \]

Height (h):

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1. What is Height of Frustum of Cone?

The height of a frustum of a cone is the perpendicular distance between its two parallel bases. It is an important geometric measurement used in various applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \sqrt{l^2 - \left( \sqrt{\frac{A_{Base}}{\pi}} - r \right)^2} \]

Where:

\( h \) — Height of frustum
\( l \) — Slant height
\( A_{Base} \) — Area of the base circle
\( r \) — Radius of the top circle
\( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: The formula calculates the height using the slant height and the difference between the base and top radii.

3. Importance of Height Calculation

Details: Calculating the height of a frustum is essential in geometry, engineering, and architecture for determining volume, surface area, and structural properties.

4. Using the Calculator

Tips: Enter slant height, base area, and top radius. All values must be positive numbers with the top radius being less than or equal to the base radius derived from the base area.

5. Frequently Asked Questions (FAQ)

Q1: What is a frustum of a cone?
A: A frustum is the portion of a cone that remains after cutting off the top by a plane parallel to the base.

Q2: Can the top radius be zero?
A: Yes, if the top radius is zero, the frustum becomes a complete cone.

Q3: What units should I use?
A: Use consistent units for all measurements (e.g., all in meters or all in inches).

Q4: What if the calculated height is imaginary?
A: An imaginary height indicates invalid input where the slant height is insufficient for the given radii difference.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact based on the input values, using precise geometric relationships.