cylinder

The volume and area of a cylinder are given by simple formulae relating the dimensions of the cylinder.

In geometry, a prism with a circular cross-section. In everyday use, the term applies to a right cylinder, in which the curved surface is perpendicular to the base.

As it is a prism, the volume (V) of a cylinder is area of cross-section (πr²) × height (h), or

V = πr²h

where r is the radius of the base and h is the height of the cylinder.

Its total surface area (A) = the curved surface area + the area of both circular ends. To find the curved surface area, the hollow cylinder area should be imagined stretched flat to form a rectangle:

Curved surface area = circumference × h, or 2πr × h

Area both circular ends = 2 × πr²

So A = 2πr² + 2πrh

and by factorizing:

A = 2πr(h + r)

As an example, using the formulae for volume and surface area, it is possible to calculate (a) the surface area of a pot that needs to be painted, and (b) the maximum volume of water the pot can hold. The pot has an external diameter of 9 cm, an internal diameter of 8 cm, and a height of 12 cm:

(a) Only one end of the pot needs to be painted, so the formula for the surface area (A) is:

A = πr² + 2πrh, or

A = πr(r + 2h), so

A = π × 4.5(4.5 + (2 × 12)) = π × 4.5 × 28.5

A = 402.9 cm² (to 1 decimal place)

(b) The formula for the volume (V) is V = πr2h, so

V = π × 4² × 12

V = 603.2 cm³