1. What is the Height of a Cone?

The height of a cone is the perpendicular distance from the base to the apex (vertex) of the cone. It's an important measurement in geometry and engineering when working with conical shapes.

2. How Does the Calculator Work?

The calculator uses the cone height formula:

Where:

• \( h \) — Height of the cone (length units)
• \( V \) — Volume of the cone (cubic units)
• \( r \) — Radius of the base (length units)
• \( \pi \) — Pi, approximately 3.14159

Explanation: The formula derives from the volume formula of a cone (\( V = \frac{1}{3}\pi r^2 h \)), rearranged to solve for height.

3. Importance of Height Calculation

Details: Calculating the height of a cone is essential in various applications including construction, manufacturing, and design where conical shapes are used (funnels, traffic cones, storage tanks, etc.).

4. Using the Calculator

Tips: Enter the volume in cubic units and radius in length units. Both values must be positive numbers. The calculator will compute the height in the same length units as the radius.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the slant height instead of radius?
A: You'll need additional information. The slant height relates to both height and radius through the Pythagorean theorem (\( l = \sqrt{r^2 + h^2} \)).

Q2: Does the calculator work for truncated cones?
A: No, this calculator is for regular cones. Truncated cones (frustums) require different formulas accounting for both top and bottom radii.

Q3: What units should I use?
A: Use consistent units - the volume should be in cubic units of whatever length unit you use for radius (e.g., if radius is in cm, volume should be in cm³).

Q4: How precise is the calculation?
A: The calculator uses PHP's pi() function (approximately 3.1415926535898) and provides results rounded to 2 decimal places.

Q5: Can I use this for oblique cones?
A: No, this formula is for right circular cones where the apex is directly above the center of the base.