Question

formula for a cylinder

Answer 1

Common formulas for a right circular cylinder (radius r, height h):

- Volume:
V = π r^2 h

- Lateral (curved) surface area:
A_lateral = 2 π r h

- Total surface area (includes top and bottom):
A_total = 2 π r^2 + 2 π r h = 2 π r (r + h)

If you know the diameter d instead of r: r = d/2, so V = π d^2 h / 4.

Hollow (cylindrical shell) with outer radius R and inner radius r:
- Volume = π (R^2 − r^2) h
- Lateral area = 2 π (R + r) h (if including inner and outer curved surfaces, add top/bottom as needed)

Cartesian equation of a right circular cylinder whose axis is z and radius r:
- x^2 + y^2 = r^2 (with z between z0 and z0 + h to get a finite cylinder).

If you want an example or a formula for an oblique cylinder, tell me the values or specify which case.