A cylinder is a three-dimensional solid shape that consists of two parallel circular bases connected by a curved surface. Finding the volume of a cylinder is a fundamental skill in geometry, physics, and engineering.
V = π × r² × h
To use this formula, you need two primary measurements:
Radius (r): The distance from the center of the circular base to its edge.
Height (h): The vertical distance between the two circular bases.
π (Pi): A mathematical constant approximately equal to 3.14159.
Step-by-Step Calculation Guide
Measure the Radius: If you only have the diameter (the distance across the circle through the center), divide it by 2 to get the radius.
Square the Radius: Multiply the radius by itself (r × r).
Multiply by Pi: Multiply your squared radius by 3.14159. This gives you the area of the circular base.
Multiply by Height: Finally, multiply that base area by the height of the cylinder to find the total volume.
Practical Example
Scenario: You have a water tank with a radius of 3 meters and a height of 5 meters.
1. Radius squared: 3 × 3 = 9
2. Area of base: 9 × 3.14159 = 28.274 m²
3. Total Volume: 28.274 × 5 = 141.37 cubic meters
Why Calculate Cylinder Volume?
Calculating volume is essential in various real-world applications:
Construction: Determining the amount of concrete needed for circular pillars.
Manufacturing: Calculating the capacity of soda cans, fuel tanks, or pipes.
Cooking: Finding out how much liquid a cylindrical pot can hold.
Logistics: Estimating space for shipping cylindrical containers or barrels.
Surface Area Calculation
While volume measures the space inside, surface area measures the total area of the outside faces. The formula for the total surface area of a cylinder is:
A = 2πrh + 2πr²
This includes the area of the two circular ends (2πr²) plus the area of the side (2πrh).
function calculateCylinderVolume() {
var r = document.getElementById("calc_radius").value;
var h = document.getElementById("calc_height").value;
var unit = document.getElementById("calc_unit").value;
var decimals = document.getElementById("calc_decimal").value;
var radius = parseFloat(r);
var height = parseFloat(h);
var precision = parseInt(decimals);
if (isNaN(radius) || isNaN(height) || radius <= 0 || height <= 0) {
alert("Please enter valid positive numbers for both radius and height.");
return;
}
// Volume Calculation: V = PI * r^2 * h
var volume = Math.PI * Math.pow(radius, 2) * height;
// Surface Area Calculation: A = 2*PI*r*h + 2*PI*r^2
var surfaceArea = (2 * Math.PI * radius * height) + (2 * Math.PI * Math.pow(radius, 2));
var volumeDisplay = volume.toFixed(precision);
var saDisplay = surfaceArea.toFixed(precision);
document.getElementById("volumeValue").innerText = volumeDisplay + " " + unit + "³";
document.getElementById("surfaceAreaValue").innerText = saDisplay + " " + unit + "²";
document.getElementById("volumeResult").style.display = "block";
// Smooth scroll to result
document.getElementById("volumeResult").scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}