Slant Height of Cone given Height and Base Circumference Calculator

Formula Used:

\[ \text{Slant Height of Cone} = \sqrt{\text{Height of Cone}^2 + \left(\frac{\text{Base Circumference of Cone}}{2\pi}\right)^2} \]

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 base. It can be calculated using the Pythagorean theorem when the height and base circumference are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Slant Height} = \sqrt{h^2 + \left(\frac{C}{2\pi}\right)^2} \]

Where:

\( h \) — Height of the cone (m)
\( C \) — Base circumference of the cone (m)
\( \pi \) — Mathematical constant approximately equal to 3.14159

Explanation: The formula first calculates the radius from the circumference, then applies the Pythagorean theorem to find the slant height.

3. Importance of Slant Height Calculation

Details: The slant height is crucial for calculating the lateral surface area of a cone and is used in various engineering and architectural applications involving conical structures.

4. Using the Calculator

Tips: Enter the height and base circumference in meters. Both values must be positive numbers. The calculator will compute the slant height using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between slant height and height?
A: The slant height is always greater than or equal to the height of the cone, as it represents the hypotenuse of the right triangle formed by the height and radius.

Q2: Can this formula be used for truncated cones?
A: No, this formula is specifically for right circular cones. Truncated cones have a different formula for calculating slant height.

Q3: What units should be used for input values?
A: The calculator accepts any consistent units, but the result will be in the same units as the input. Meters are recommended for SI units.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, assuming precise input values. The result is rounded to 6 decimal places for clarity.

Q5: What if I know the radius instead of circumference?
A: If you know the radius, you can use the simpler formula: Slant Height = √(h² + r²), where r is the radius.