Question

V = π r^2 h.

Informal argument: We could also think of the cylinder as a stack of thin circular disks, each with area πr2. Summing up the volumes of those disks over the height h gives volume = ∫0h πr2 dz = πr2h. Alternatively, as with any prism the volume is just base area, here the circle of area πr2, times height:

Answer 1

Yes — both are correct. For a right circular cylinder of constant radius r and height h:

- Slice method (calculus/Riemann sums): each thin disk at height z has volume ≈ area · thickness = πr^2 dz, so integrating from 0 to h gives V = ∫0^h πr^2 dz = πr^2 h.

- Geometric/prism argument: a prism has volume = base area × height. A cylinder is a prism whose base is a circle of area πr^2, hence V = (πr^2)h = πr^2 h.

(Assumes r is constant along the axis; otherwise one must integrate a(z) dz where a(z) is the cross‑sectional area.)