Hollow Cylinder Volume Calculator

Ever glanced at a paper towel tube or a steel pipe and thought—how much actual material is in there? Not just the outer shape, but the solid part that’s doing the work? That’s where understanding the volume of a hollow cylinder becomes incredibly practical.

Whether it’s plumbing, telescopes, bike frames, or industrial piping, hollow cylinders are a fundamental part of modern design. And whether you're a student, an engineer, or just someone who enjoys knowing how things work, calculating the volume of one is easier than you might think—and seriously useful. For other shapes—solid or hollow—the Volume Calculator has options for cones, spheres, prisms, and more.

What Is a Hollow Cylinder?

Let’s break it down simply. A hollow cylinder is a tube-like structure with an empty core. Think of a drinking straw, a PVC pipe, or the cardboard roll inside foil wrap. It looks like a regular cylinder but has a cylindrical gap running through its center.

Geometrically, a hollow cylinder is defined by three key values:

• R = outer radius

• r = inner radius

• h = height of the cylinder

To visualize it, imagine drilling a smaller cylinder through the center of a larger solid one. The remaining material—the "ring" between the inner and outer walls—is what we’re calculating. Need that result in gallons, liters, or cubic inches? The Volume Converter makes switching units simple.

How to Calculate the Volume of a Hollow Cylinder

So, how do you find the volume of a hollow cylinder?

Here’s the formula:

Volume = π × h × (R² - r²)

Where:

• π (pi) ≈ 3.1416

• h: Height of the cylinder

• R: outer radius

• r: inner radius

Essentially, you’re subtracting the volume of the inner (empty) cylinder from the outer solid one, leaving you with just the usable volume of the material.

Let’s say you’re making a pipe that’s:

• 10 cm in height

• Has an outer radius of 5 cm

• And an inner radius of 3 cm

Step 1: Apply the values
Volume = π × 10 × (5² - 3²)
= π × 10 × (25 - 9)
= π × 10 × 16
= 160π

Step 2: Multiply by π
≈ 160 × 3.1416 = 502.65 cm³

So, your hollow pipe contains roughly 502.65 cubic centimeters of material. That’s the volume of the actual material needed—critical for manufacturing costs, structural weight, or shipping estimates. 

How the Romans Engineered with Hollow Cylinders

Let’s rewind 2,000 years to ancient Rome—an empire known for aqueducts that revolutionized urban life by delivering fresh water over long distances. These systems weren’t just open-air channels. In rugged or underground sections, Roman engineers needed pressurized conduits that wouldn’t crack or collapse.

So, what did they use?

Hollow lead pipes.

These cylindrical structures had carefully measured inner and outer diameters—centuries before modern formulas existed. Ancient Roman builders used techniques remarkably close to today's hollow cylinder volume calculations to estimate how much lead was needed for construction.

They didn’t yet know about lead poisoning, but they clearly understood engineering efficiency. Hollow pipes meant less material, reduced weight, and easier transport—principles still used in design today.

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