1. What is the Cone Volume Formula?

The volume of a cone is calculated using the formula \( V = \frac{1}{3} \pi r^2 h \), where r is the radius of the base and h is the height of the cone. This formula shows that a cone's volume is exactly one third of 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 length units)
• \( r \) — Radius of the base (length units)
• \( h \) — Height of the cone (length units)
• \( \pi \) — Approximately 3.14159

Explanation: The formula calculates the space occupied by a right circular cone, which tapers smoothly from a flat base to a point called the apex.

3. Importance of 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 the same length units. The result will be in cubic units of whatever length unit you used. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between height and slant height?
A: Height is the perpendicular distance from base to apex, while slant height is the distance along the cone's side from base to apex.

Q2: Does this 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.

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

Q4: How precise is this calculation?
A: The calculator uses PHP's pi() function which provides sufficient precision for most practical applications.

Q5: Can I use different units for radius and height?
A: No, both measurements must be in the same units for the calculation to be valid.