Slant Height of Truncated Cone given Curved Surface Area Calculator

Formula Used:

\[ \text{Slant Height} = \frac{\text{Curved Surface Area}}{\pi \times (\text{Base Radius} + \text{Top Radius})} \]

Slant Height (hSlant):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Slant Height of Truncated Cone?

The Slant Height of a Truncated Cone is the length of the straight line connecting any point on the base to the truncated top circular face of the Truncated Cone. It represents the diagonal distance along the lateral surface.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Slant Height} = \frac{\text{Curved Surface Area}}{\pi \times (\text{Base Radius} + \text{Top Radius})} \]

Where:

Curved Surface Area — The area of the lateral surface of the truncated cone (m²)
Base Radius — Radius of the base circular surface (m)
Top Radius — Radius of the top circular surface (m)
π — Archimedes' constant (approximately 3.14159)

Explanation: This formula derives from the relationship between the curved surface area and the slant height in a truncated cone geometry.

3. Importance of Slant Height Calculation

Details: Calculating the slant height is essential for various engineering and architectural applications, including surface area calculations, material estimation, and structural design of conical frustums.

4. Using the Calculator

Tips: Enter curved surface area in square meters, base radius in meters, and top radius in meters. All values must be positive, and the sum of base and top radii must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a truncated cone?
A: A truncated cone (or conical frustum) is a cone with the tip cut off by a plane parallel to the base, resulting in two parallel circular faces.

Q2: How is this different from a regular cone's slant height?
A: For a regular cone, the formula is simpler: Slant Height = √(Height² + Radius²). The truncated cone formula accounts for two different radii.

Q3: Can this calculator handle different units?
A: The calculator uses meters for length units. Convert all measurements to meters before calculation for accurate results.

Q4: What if both radii are zero?
A: The sum of radii cannot be zero as it would make the denominator zero, which is mathematically undefined. At least one radius must be positive.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of truncated cones, assuming precise input values.