Height of Frustum of Cone given Total Surface Area, Top Area and Base Area Calculator

Formula Used:

\[ h = \frac{3V}{\pi (r_1^2 + r_1r_2 + r_2^2)} \]

Height (h):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Height of Frustum of Cone?

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

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{3V}{\pi (r_1^2 + r_1r_2 + r_2^2)} \]

Where:

\( h \) — Height of the frustum
\( V \) — Volume of the frustum
\( r_1 \) — Top radius of the frustum
\( r_2 \) — Base radius of the frustum
\( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: This formula calculates the height of a frustum of a cone when the volume and both radii are known.

3. Importance of Height Calculation

Details: Calculating the height of a frustum is crucial in construction, manufacturing, and design applications where precise geometric measurements are required for structural integrity and proper fitting.

4. Using the Calculator

Tips: Enter the volume in cubic meters, top radius in meters, and base radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: Can this calculator handle different units?
A: The calculator uses meters as the default unit. Ensure all measurements are in consistent units for accurate results.

Q3: What if both radii are equal?
A: If both radii are equal, the frustum becomes a cylinder, and the formula simplifies accordingly.

Q4: Is there a minimum volume requirement?
A: The volume must be greater than zero for the calculation to be valid.

Q5: Can this formula be used for other shapes?
A: This specific formula is designed only for frustums of right circular cones.