1. What is the Cone Volume Formula?

The volume of a cone is given by one-third the product of its base area (πr²) and height (h). This formula is derived from calculus or by comparing a cone to a cylinder with the same base and height.

2. How Does the Calculator Work?

The calculator uses the cone volume formula:

Where:

• \( V \) — Volume (cubic units)
• \( r \) — Radius of the base (units)
• \( h \) — Height of the cone (units)
• \( \pi \) — Approximately 3.14159

Explanation: The formula calculates the space occupied by a right circular cone, where the base is a perfect circle and the apex is directly above the center of the base.

3. Importance of Cone Volume Calculation

Details: Calculating cone volume is essential in geometry, engineering, and various practical applications like determining capacity of conical containers, construction materials, or geological formations.

4. Using the Calculator

Tips: Enter the radius and height in consistent units (both in meters, inches, etc.). The calculator will output volume in cubic units of the same measurement system.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for oblique cones?
A: No, this formula is specifically for right circular cones where the apex is directly above the center of the base.

Q2: How is this formula related to pyramid volume?
A: Both follow the same principle: (1/3) × base area × height. For pyramids the base is a polygon, while for cones it's a circle.

Q3: What if I only have diameter instead of radius?
A: Simply divide the diameter by 2 to get the radius before using the calculator.

Q4: Can I use this for truncated cones (frustums)?
A: No, frustums require a different formula accounting for both top and bottom radii.

Q5: Why is there a 1/3 in the formula?
A: A cone occupies exactly one-third the volume of a cylinder with the same base and height.