1. What is Volume of Frustum of Cone?

The volume of a frustum of a cone is the amount of space enclosed by the frustum. A frustum is created when a plane cuts off the top of a cone parallel to its base.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of the frustum
• \( h \) — Height of the frustum
• \( r \) — Top radius of the frustum
• \( R \) — Base radius of the frustum
• \( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: The formula calculates the volume by taking one-third of the product of the height and the sum of the squares of the radii plus their product.

3. Importance of Volume Calculation

Details: Calculating the volume of a frustum of a cone is important in various fields including engineering, architecture, and manufacturing where conical shapes are commonly used.

4. Using the Calculator

Tips: Enter the height, top radius, and base radius in consistent units. All values must be positive numbers with the base radius typically being larger than the top radius.

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: If the top radius is zero, the frustum becomes a complete cone. However, for this calculator, the top radius should be ≥0 and base radius >0.

Q3: What units should I use?
A: You can use any consistent units (cm, m, inches, etc.). The volume result will be in cubic units of your input.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact based on the formula, assuming perfect geometric shapes.

Q5: Can I use this for truncated pyramids?
A: No, this formula is specifically for conical frustums. Pyramids have different volume formulas.