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Cylinder Volume Without Top and Bottom

Removing the top and bottom of a cylinder doesn't change its volume — the enclosed space stays the same. What does change is the surface area. This page covers both calculations and explains when the distinction matters.

Volume Without Top & Bottom

V = πr²h, LSA = 2πrh
✕ ✕ LSA = 2πrh Open tube — same volume

Volume Stays the Same

✕ ✕ V = πr²h (same)

Volume measures the space inside the cylinder, not the material of the cylinder walls. Whether the cylinder has caps or not, the enclosed space is the same:

V = πr²h

A pipe (no caps) and a sealed can (with caps) of the same dimensions hold the same volume. The caps don't add or subtract from the internal space — they only seal it.

So if someone asks for the 'volume of a cylinder without top and bottom,' the answer is the same as any cylinder: V = πr²h.

Surface Area Without Caps

lateral πr² πr² LSA = 2πrh (no caps)

What does change is the surface area. A full cylinder has: Total SA = 2πr² + 2πrh (two bases + curved side)

Without one cap (open top): SA = πr² + 2πrh

Without both caps (open tube): SA = 2πrh (lateral surface area only)

This matters for material calculations — how much sheet metal, fabric, or paint you need to cover the cylinder. An open tube uses significantly less material than a sealed cylinder.

Example: r = 10 cm, h = 30 cm. Full SA = 2π(100) + 2π(300) = 2,513.3 cm². Without caps: SA = 2π(300) = 1,884.9 cm² — about 25% less material.

Practical Examples

Tubes • Chimneys • Pipes

Pipes and tubes: Open on both ends. Volume = πr²h, surface area = 2πrh.

Drinking glasses and cups: Open on top, closed on bottom. Volume = πr²h, surface area = πr² + 2πrh.

Cans and sealed containers: Closed on both ends. Volume = πr²h, surface area = 2πr² + 2πrh.

Sleeves, rings, and cylindrical molds: Often open-ended. For material weight, use the lateral surface area × thickness × density.

In all cases, the volume formula is identical — V = πr²h. Only the surface area calculation changes based on which ends are open or closed.

Frequently Asked Questions

Does removing the top and bottom change the volume?
No. Volume is the space enclosed by the cylinder shape, not the material. V = πr²h regardless of whether the ends are open or closed.
What is the surface area of a cylinder without top and bottom?
The lateral surface area: SA = 2πrh. This is just the curved side.
How is an open cylinder different from a closed one?
They have the same volume. The difference is surface area: a closed cylinder includes the two circular bases (adding 2πr²), while an open one has only the lateral surface.
How do I calculate material for an open-ended cylinder?
Calculate the lateral surface area (2πrh) and multiply by the material thickness to get the volume of material. Then multiply by density for weight.
Is a pipe a cylinder without top and bottom?
Yes. A pipe is an open-ended hollow cylinder. Its internal volume is πr²h (using the inner radius). Its material surface area is the sum of inner and outer lateral surfaces plus the two ring-shaped ends.