Volume of Truncated Cone given Slant Height Calculator

Formula Used:

\[ V = \frac{\pi}{3} \times (r_{Base}^2 + (r_{Base} \times r_{Top}) + r_{Top}^2) \times \sqrt{h_{Slant}^2 - (r_{Base} - r_{Top})^2} \]

Base Radius of Truncated Cone:

Top Radius of Truncated Cone:

Slant Height of Truncated Cone:

Volume of Truncated Cone:

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1. What is Volume of Truncated Cone?

The volume of a truncated cone (frustum) is the total quantity of three dimensional space enclosed by the entire surface of the truncated cone. It represents the capacity or amount of material that the truncated cone can hold.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{\pi}{3} \times (r_{Base}^2 + (r_{Base} \times r_{Top}) + r_{Top}^2) \times \sqrt{h_{Slant}^2 - (r_{Base} - r_{Top})^2} \]

Where:

\( V \) — Volume of Truncated Cone (m³)
\( r_{Base} \) — Base Radius of Truncated Cone (m)
\( r_{Top} \) — Top Radius of Truncated Cone (m)
\( h_{Slant} \) — Slant Height of Truncated Cone (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the volume of a truncated cone using the base radius, top radius, and slant height, incorporating the mathematical constant π and square root function.

3. Importance of Volume Calculation

Details: Calculating the volume of truncated cones is crucial in various engineering, architectural, and manufacturing applications where this geometric shape is used, such as in storage tanks, funnels, and structural components.

4. Using the Calculator

Tips: Enter base radius, top radius, and slant height in meters. All values must be positive numbers, and the slant height must be greater than the difference between base and top radii.

5. Frequently Asked Questions (FAQ)

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

Q2: Can the top radius be zero?
A: No, the top radius must be greater than or equal to zero. If zero, it becomes a complete cone rather than a truncated cone.

Q3: What units should I use?
A: The calculator uses meters for all dimensions, but you can use any consistent unit as long as all inputs are in the same unit.

Q4: What if the slant height is too short?
A: The slant height must be greater than the difference between base and top radii for the calculation to be valid (real number result).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric shapes, using the precise value of π and square root function.