Slant Height of Frustum of Cone given Total Surface Area, Top Area and Base Area Calculator

Formula Used:

\[ h_{slant} = \frac{TSA - A_{Top} - A_{Base}}{\pi \times (r_{Top} + r_{Base})} \]

Total Surface Area (TSA):

m²

Top Area (A_Top):

m²

Base Area (A_Base):

m²

Top Radius (r_Top):

Base Radius (r_Base):

Slant Height (h_slant):

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1. What is Slant Height of Frustum of Cone?

The slant height of a frustum of a cone is the shortest distance between the edges of the two bases along the lateral surface. It's an important measurement in geometry and engineering applications involving conical sections.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{slant} = \frac{TSA - A_{Top} - A_{Base}}{\pi \times (r_{Top} + r_{Base})} \]

Where:

\( h_{slant} \) — Slant height of the frustum
\( TSA \) — Total surface area of the frustum
\( A_{Top} \) — Area of the top circular base
\( A_{Base} \) — Area of the bottom circular base
\( r_{Top} \) — Radius of the top circular base
\( r_{Base} \) — Radius of the bottom circular base
\( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: The formula calculates slant height by subtracting the areas of the two bases from the total surface area, then dividing by the circumference of the average radius.

3. Importance of Slant Height Calculation

Details: Accurate slant height calculation is crucial for determining the lateral surface area, volume, and other geometric properties of conical frustums in architectural, engineering, and manufacturing applications.

4. Using the Calculator

Tips: Enter all values in consistent units (meters recommended). Ensure all values are positive and the total surface area is greater than the sum of the two base areas.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between slant height and height?
A: Slant height is the distance along the lateral surface, while height is the perpendicular distance between the two bases.

Q2: Can this formula be used for complete cones?
A: Yes, for a complete cone, the top area would be zero, and the formula still applies.

Q3: What if I only have diameters instead of radii?
A: Convert diameters to radii by dividing by 2 before entering the values.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming perfect geometric shapes and accurate input values.

Q5: What units should I use?
A: Use consistent units throughout (all meters, all centimeters, etc.). The result will be in the same linear unit as the radius inputs.