Slant Height of Cone given Total Surface Area and Base Area Calculator

Formula Used:

\[ \text{Slant Height of Cone} = \frac{\text{Total Surface Area of Cone}}{\sqrt{\pi \times \text{Base Area of Cone}}} - \sqrt{\frac{\text{Base Area of Cone}}{\pi}} \]

Slant Height of Cone:

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1. What is the Slant Height of Cone Formula?

The slant height of a cone is the distance from the apex to any point on the circumference of the circular base. This formula calculates the slant height when the total surface area and base area are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Slant Height} = \frac{\text{Total Surface Area}}{\sqrt{\pi \times \text{Base Area}}} - \sqrt{\frac{\text{Base Area}}{\pi}} \]

Where:

Total Surface Area (TSA) - The total surface area of the cone (m²)
Base Area (ABase) - The area of the circular base of the cone (m²)
π - Archimedes' constant (approximately 3.14159)

Explanation: The formula derives from the relationship between the total surface area, base area, and slant height of a cone.

3. Importance of Slant Height Calculation

Details: Calculating the slant height is essential in geometry and engineering applications where cone measurements are required, such as in construction, manufacturing, and design.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: The calculator expects inputs in square meters (m²) for both total surface area and base area.

Q2: Can this formula be used for truncated cones?
A: No, this formula is specifically for right circular cones, not truncated cones (frustums).

Q3: What if I only know the radius and height?
A: If you know the radius and height, you can calculate slant height using the Pythagorean theorem: √(radius² + height²).

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

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