Radius of Double Point Calculator

Formula Used:

\[ r = \sqrt{\frac{V}{\pi \times (h_{Cylinder} + \frac{h_{First Cone}}{3} + \frac{h_{Second Cone}}{3})}} \]

Volume of Double Point:

m³

Cylindrical Height:

Height of First Cone:

Height of Second Cone:

Radius of Double Point:

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1. What is Radius of Double Point?

The Radius of Double Point is the distance from center to any point on the circumference of the circular faces of the cylindrical portion in the Double Point. It's a crucial measurement for understanding the geometry of this composite shape.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ r = \sqrt{\frac{V}{\pi \times (h_{Cylinder} + \frac{h_{First Cone}}{3} + \frac{h_{Second Cone}}{3})}} \]

Where:

\( r \) — Radius of Double Point (m)
\( V \) — Volume of Double Point (m³)
\( h_{Cylinder} \) — Cylindrical Height of Double Point (m)
\( h_{First Cone} \) — Height of First Cone of Double Point (m)
\( h_{Second Cone} \) — Height of Second Cone of Double Point (m)
\( \pi \) — Archimedes' constant (approximately 3.1416)

3. Formula Explanation

Details: This formula calculates the radius by considering the total volume distribution across the cylindrical portion and two conical portions of the Double Point shape. The formula accounts for the different volume contributions of each geometric component.

4. Using the Calculator

Tips: Enter all measurements in meters. Volume must be in cubic meters, and height measurements in meters. All values must be positive numbers. The cylindrical height and cone heights can be zero, but the denominator must be greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Double Point shape?
A: A Double Point is a geometric shape consisting of a central cylindrical portion with two conical portions attached to its circular faces.

Q2: Why are the cone heights divided by 3 in the formula?
A: This accounts for the volume calculation of cones, where volume = (1/3)πr²h, making the height contribution effectively h/3 when solving for radius.

Q3: What units should I use for input?
A: Use consistent units - meters for linear measurements and cubic meters for volume. The calculator will return radius in meters.

Q4: Can I use this for other similar shapes?
A: This formula is specifically designed for the Double Point shape described. Other composite shapes may require different formulas.

Q5: What if I get an error message?
A: Ensure all input values are positive numbers and that the sum in the denominator (cylindrical height + cone heights/3) is greater than zero.