Volume Of Truncated Cone Given Curved Surface Area Calculator

Formula Used:

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

Base Radius of Truncated Cone:

Top Radius of Truncated Cone:

Curved Surface Area of Truncated Cone:

m²

Volume of Truncated Cone:

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1. What is the 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 of this geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Truncated Cone (m³)
\( r_{Base} \) — Base Radius of Truncated Cone (m)
\( r_{Top} \) — Top Radius of Truncated Cone (m)
\( CSA \) — Curved Surface Area of Truncated Cone (m²)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the volume of a truncated cone when the base radius, top radius, and curved surface area are known, using the mathematical constant π and square root function.

3. Importance of Volume Calculation

Details: Calculating the volume of truncated cones is essential 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 and top radius in meters, curved surface area in square meters. All values must be positive numbers greater than zero.

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: Why is the curved surface area needed for volume calculation?
A: The curved surface area helps determine the slant height of the truncated cone, which is necessary for calculating the volume when using this specific formula.

Q3: What are typical applications of truncated cones?
A: Truncated cones are commonly used in buckets, lampshades, storage containers, and various architectural and engineering structures.

Q4: Can this formula be used for any truncated cone?
A: Yes, this formula applies to all right circular truncated cones where the cutting plane is parallel to the base.

Q5: What if I have different units of measurement?
A: Convert all measurements to consistent units (meters for length, square meters for area) before using the calculator for accurate results.