Height Of Frustum Of Cone Given Volume, Top Area And Base Area Calculator

Formula Used:

\[ h = \frac{3V}{\pi (A_{top} + A_{base} + \sqrt{A_{top} \times A_{base}})} \]

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 its two parallel circular bases. It is an important geometric measurement used in various engineering and architectural applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h = \frac{3V}{\pi (A_{top} + A_{base} + \sqrt{A_{top} \times A_{base}})} \]

Where:

\( h \) — Height of the frustum (m)
\( V \) — Volume of the frustum (m³)
\( A_{top} \) — Area of the top circular base (m²)
\( A_{base} \) — Area of the base circular base (m²)
\( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: This formula derives from the volume formula of a frustum of a cone, rearranged to solve for height.

3. Importance of Height Calculation

Details: Calculating the height of a frustum is essential in construction, manufacturing, and design applications where precise dimensional measurements are required for conical structures and components.

4. Using the Calculator

Tips: Enter the volume in cubic meters, top area in square meters, and base area in square meters. All values must be positive numbers greater than zero.

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: How is this formula derived?
A: The formula is derived from the volume formula of a frustum: \( V = \frac{1}{3}\pi h (R^2 + Rr + r^2) \), where R and r are the radii of the base and top circles respectively.

Q3: What units should I use?
A: Use consistent units throughout (e.g., meters for length, square meters for area, cubic meters for volume). The calculator will output height in the same length unit as the input dimensions.

Q4: Can this calculator handle different units?
A: No, you must convert all measurements to the same unit system before inputting values into the calculator.

Q5: What if I have the radii instead of areas?
A: You can calculate the areas using \( A = \pi r^2 \) before using this calculator, or use the alternative formula \( h = \frac{3V}{\pi (R^2 + Rr + r^2)} \) directly.