Mensuration - Cylinder

What is a Cylinder?

A cylinder is a three dimensional solid structure formed by two parallel circular bases connected by a curved surface.

The most famous type of cylinder is Right Circular Cylinder. It is a cylinder whose bases are circular and the axis joining the two bases is perpendicular to them.
When we just mention ‘Cylinder’, we generally mean a ‘Right Circular Cylinder’.

Formulae related to Cylinder

If ‘r’ is the radius, and ‘h’ is the height of a cylinder, then:

Formula 1: Volume

Volume of cylinder = Area of base × Height = $πr^2$ × h = $πr^2h$

Volume of hollow cylinder = Volume of whole cylinder - Volume of inner empty space = $πR^2h - πr^2h = π (R^2 – r^2)h$
(where R - Radius of outer cylinder, r - Radius of inner cylinder)

Formula 2: Surface Area

Curved surface area of cylinder = Perimeter of base × Height = 2πr × h = 2πrh

Total Surface area of cylinder = Curved surface area + 2 × Area of base = 2πrh + 2$πr^2$

Curved surface area of hollow cylinder = 2πRh + 2πrh = 2π(R + r)h