How to Calculate Volume of a Cylinder

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Cylinder Volume Calculator

Centimeters (cm) Meters (m) Inches (in) Feet (ft) Millimeters (mm)

Calculation Result

How to Calculate the Volume of a Cylinder

A cylinder is a three-dimensional solid object with two parallel circular bases connected by a curved surface. Whether you are calculating the capacity of a water tank, a soda can, or a mechanical pipe, finding the volume is a fundamental geometry skill.

The Cylinder Volume Formula

To find the volume (V) of a cylinder, you need two primary measurements: the radius of the circular base and the height (the distance between the two bases). The formula is:

V = π × r² × h
  • V: Volume of the cylinder
  • π (Pi): Approximately 3.14159
  • r: Radius of the circular base (half of the diameter)
  • h: Height of the cylinder

Step-by-Step Calculation Example

Let's say you have a cylindrical water container with a radius of 5 cm and a height of 10 cm. Here is how you calculate its volume:

  1. Square the radius: 5 × 5 = 25 cm²
  2. Multiply by Pi: 25 × 3.14159 = 78.539 cm² (This is the area of the base)
  3. Multiply by the height: 78.539 × 10 = 785.39 cm³

The total volume of the container is 785.39 cubic centimeters.

Practical Applications

Calculating cylinder volume is useful in many real-world scenarios:

  • Construction: Determining how much concrete is needed for a cylindrical pillar.
  • Cooking: Finding the capacity of round pots and pans.
  • Manufacturing: Designing canisters, cans, and drums for liquid storage.
  • Hydraulics: Calculating the displacement of a hydraulic piston.

Frequently Asked Questions

Q: What if I only have the diameter?
A: Simply divide the diameter by 2 to get the radius. If the diameter is 10 cm, the radius is 5 cm.

Q: What are the units for volume?
A: Volume is always expressed in cubic units (e.g., cm³, m³, in³, or ft³).

Q: How do I find the surface area?
A: The total surface area formula is 2πrh + 2πr². This includes the area of the two circular bases and the side (lateral) area.

function calculateCylinderVolume() { var radius = parseFloat(document.getElementById('radius').value); var height = parseFloat(document.getElementById('height').value); var unit = document.getElementById('unit').value; var resultDiv = document.getElementById('cylinder-result'); var volumeOutput = document.getElementById('volume-output'); var surfaceAreaOutput = document.getElementById('surface-area-output'); if (isNaN(radius) || isNaN(height) || radius <= 0 || height <= 0) { alert("Please enter positive numeric values for both radius and height."); resultDiv.style.display = "none"; return; } var pi = Math.PI; // Formula: V = pi * r^2 * h var volume = pi * Math.pow(radius, 2) * height; // Formula for Surface Area: 2*pi*r*h + 2*pi*r^2 var surfaceArea = (2 * pi * radius * height) + (2 * pi * Math.pow(radius, 2)); volumeOutput.innerHTML = "Volume: " + volume.toLocaleString(undefined, {maximumFractionDigits: 3}) + " " + unit + "³"; surfaceAreaOutput.innerHTML = "Total Surface Area: " + surfaceArea.toLocaleString(undefined, {maximumFractionDigits: 3}) + " " + unit + "²"; resultDiv.style.display = "block"; }

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