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Volume of a Cylinder Calculator

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Created by: Isabelle Clarke

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Calculate the volume of a cylinder using its radius and height. Features formula, step-by-step example, applications, and a 3D visualization.

What is a Volume of a Cylinder Calculator?

A Volume of a Cylinder Calculator is a tool used to determine the amount of space occupied by a three-dimensional cylindrical object. A cylinder is characterized by two parallel circular bases and a curved surface connecting them. This calculator requires the radius (or diameter) of the circular base and the height of the cylinder to compute its volume.

It is widely used in mathematics, engineering, physics, construction, and everyday situations where one needs to find the capacity of cylindrical containers (like tanks, pipes, cans) or the amount of material in a cylindrical shape.

Formula for the Volume of a Cylinder

The primary formula to calculate the volume of a cylinder is:

  • Volume (V): V = πr²h

Where:

  • V = Volume of the cylinder
  • π (pi) ≈ 3.14159265359 (The calculator uses a more precise value of Math.PI)
  • r = Radius of the circular base of the cylinder
  • h = Height of the cylinder (the perpendicular distance between the two bases)

If the diameter (d) is known instead of the radius (r), recall that r = d/2. The formula can then be expressed as: V = π(d/2)²h = (πd²h)/4.

How to Calculate the Volume of a Cylinder: Example

Consider a cylinder with a radius of 4 cm and a height of 10 cm.

  1. Identify the radius (r) and height (h): r = 4 cm, h = 10 cm
  2. Apply the volume formula V = πr²h: V = π × (4 cm)² × 10 cm
  3. Calculate the square of the radius: (4 cm)² = 16 cm²
  4. Multiply by π and the height: V = π × 16 cm² × 10 cm = 160π cm³
  5. Calculate the final volume (using π ≈ 3.14159): V ≈ 160 × 3.14159 cm³ ≈ 502.65 cm³

So, the volume of the cylinder is approximately 502.65 cubic centimeters.

Common Applications

Calculating the volume of a cylinder is crucial in numerous fields:

  • Engineering: Designing pipes, tanks, hydraulic cylinders, and pressure vessels.
  • Construction: Estimating materials for concrete pillars, wells, or circular foundations.
  • Manufacturing: Determining the capacity of cans, bottles, barrels, and other cylindrical containers.
  • Physics: Calculating fluid displacement, buoyancy, or material density.
  • Chemistry: Measuring liquids in cylindrical beakers or calculating reactant volumes in cylindrical reactors.
  • Agriculture: Estimating the capacity of silos or water tanks.

Sources and References

  1. Stewart, J. (2015). *Calculus: Early Transcendentals*. Cengage Learning. (Covers methods for finding volumes of solids, including cylinders).
  2. Tipler, P. A., & Mosca, G. (2007). *Physics for Scientists and Engineers*. W. H. Freeman. (Basic geometric formulas used in physics).
  3. Weisstein, Eric W. "Cylinder." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cylinder.html