1. What is the Cone Volume Formula?

The cone volume formula calculates the space occupied by a right circular cone. It's derived from the more general principle that the volume of a pyramid is one-third the base area times the height.

2. How Does the Calculator Work?

The calculator uses the cone volume formula:

Where:

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

Explanation: The formula calculates the area of the circular base (πr²), multiplies by the height, and takes one-third of that product.

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 or amount of material needed.

4. Using the Calculator

Tips: Enter radius and height in consistent units. The result will be in cubic units of whatever unit you used for input.

5. Frequently Asked Questions (FAQ)

Q1: 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.

Q2: What if my cone is in inches but I want the volume in gallons?
A: First calculate in cubic inches, then convert using appropriate conversion factors (231 cubic inches = 1 US gallon).

Q3: How precise is π in this calculation?
A: The calculator uses PHP's pi() function which is precise to about 14 decimal places.

Q4: Can I use diameter instead of radius?
A: Yes, but you'll need to divide diameter by 2 first (r = d/2).

Q5: What about truncated cones (frustums)?
A: Frustums require a different formula: V = (1/3)πh(r₁² + r₁r₂ + r₂²) where r₁ and r₂ are the two radii.