Calculate the radius of a cylinder given its volume and height, or its circumference.
Volume and Height
Circumference
Understanding Cylinder Radius Calculation
A cylinder is a fundamental geometric shape characterized by two parallel circular bases connected by a curved surface. Key dimensions of a cylinder include its height and its radius (or diameter). The radius, denoted by 'r', is the distance from the center of a circular base to any point on its edge. It is a crucial parameter in calculating various properties of the cylinder, such as its volume, surface area, and the area of its bases.
Calculating Radius from Volume and Height
The volume (V) of a cylinder is given by the formula:
V = π * r² * h
Where:
V is the Volume of the cylinder
π (Pi) is a mathematical constant, approximately 3.14159
r is the Radius of the cylinder's base
h is the Height of the cylinder
To find the radius (r) when the Volume (V) and Height (h) are known, we can rearrange the formula:
r² = V / (π * h)
And then take the square root:
r = √(V / (π * h))
It's important to ensure that the units for volume and height are consistent (e.g., cubic meters and meters, or cubic feet and feet). The resulting radius will be in the linear unit corresponding to the height (e.g., meters or feet).
Calculating Radius from Circumference
The circumference (C) of a circle (which is the perimeter of the cylinder's base) is given by the formula:
C = 2 * π * r
Where:
C is the Circumference of the circle
π (Pi) is a mathematical constant, approximately 3.14159
r is the Radius of the circle
To find the radius (r) when the Circumference (C) is known, we rearrange the formula:
r = C / (2 * π)
Ensure that the unit for circumference is a linear unit (e.g., meters, inches, feet). The resulting radius will have the same unit.
Use Cases
Calculating the radius of a cylinder is essential in various fields:
Engineering and Manufacturing: Designing pipes, tanks, and cylindrical components.
Physics: Calculating properties of cylindrical objects in experiments or simulations.
Architecture: Designing cylindrical structures like silos, water towers, or columns.
Mathematics: Solving geometry problems and understanding spatial relationships.
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var radius;
var pi = Math.PI;
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var radiusSquared = volume / (pi * height);
radius = Math.sqrt(radiusSquared);
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