Volume of a hollow pipe

Subtract the inner cylinder from the outer: V = π(R² − r²)h.

Key formulas

Outer radius R, inner radius r, length (or height) h. Metal volume is the difference of two solid cylinders.

R=5, r=3, h=20 → V=π(25−9)×20=320π.

If thickness t is given, r = R − t (for a circular pipe). Convert units before subtracting.

Problem. A hollow pipe has outer radius 5 cm, inner radius 3 cm and length 20 cm. Find the volume of metal in terms of π.

Solution. V = π(R² − r²)h = π(25 − 9)×20 = 320π cm³.

R²−r²=(R−r)(R+r) can help with mental arithmetic.

Outer radius 6, inner 4, length 10. Metal volume is:

Yes — the distance along the axis.