Circumference to Volume Calculator

The Circumference to Volume Calculator is a helpful tool for calculating the volume of shapes like spheres, cylinders, and cones, using the circumference as the primary input. This tool simplifies complex formulas, saving time and effort for users. It is widely used in mathematics, engineering, and construction, where accurate volume calculations are required.

This calculator falls under the "Geometry and Measurement Tools" category.

Formulas for Circumference to Volume Calculation

The following formulas are used by the calculator:

Sphere: Radius from circumference: r = c / (2π) Volume from radius: V = (4/3)πr³ Combined formula: V = (4/3)π(c/(2π))³

Cylinder: Radius from circumference: r = c / (2π) Volume from radius and height: V = πr²h Combined formula: V = π(c/(2π))²h

Cone: Radius from circumference: r = c / (2π) Volume from radius and height: V = (1/3)πr²h Combined formula: V = (1/3)π(c/(2π))²h

Note: In these formulas:

• c is the circumference
• r is the radius
• h is the height
• π is the mathematical constant pi (approximately 3.14159)

Conversion Table for Common Circumference Values

Below is a table to help users find approximate volumes for common circumferences without needing to calculate.

Shape	Circumference (c)	Radius (r)	Height (h)	Volume Formula	Volume (V) Approximation
Sphere	31.42	5	N/A	V = (4/3)πr³	523.6 cm³
Cylinder	31.42	5	10	V = πr²h	785.4 cm³
Cone	31.42	5	10	V = (1/3)πr²h	261.8 cm³

Example of Circumference to Volume Calculator

Imagine you have a sphere with a circumference of 31.42 cm. Using the formulas:

1. Radius: r = 31.42 / (2 × 3.14159) = 5 cm
2. Volume: V = (4/3) × 3.14159 × (5³) = 523.6 cm³

Thus, the sphere's volume is approximately 523.6 cubic centimeters.

Most Common FAQs