1. What is the Height of Cone Formula?

The formula calculates the height of a cone when given its total surface area and base radius. It's derived from the standard cone surface area formula and provides an accurate measurement of the vertical height of the cone.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Cone (m)
• \( TSA \) — Total Surface Area of Cone (m²)
• \( r_{Base} \) — Base Radius of Cone (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula rearranges the total surface area equation to solve for height, using algebraic manipulation and square root operations.

3. Importance of Height Calculation

Details: Calculating the height of a cone is essential in geometry, engineering, and construction applications where precise dimensional measurements are required for cone-shaped objects.

4. Using the Calculator

Tips: Enter total surface area in square meters and base radius in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: Use consistent units (meters for both radius and height, square meters for surface area) for accurate results.

Q2: Can this formula be used for truncated cones?
A: No, this formula is specifically for complete, right circular cones. Different formulas apply to truncated cones.

Q3: What if I get a negative value under the square root?
A: This indicates invalid input values that don't correspond to a real cone. Check that your surface area and radius values are consistent.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact based on the input values, using the precise value of π for maximum accuracy.

Q5: Can this calculator handle very large or small values?
A: Yes, the calculator can process a wide range of values as long as they are positive numbers.