Cylinder (geometry) - Common Use

Common Use

In common use a cylinder is taken to mean a finite section of a right circular cylinder, i.e., the cylinder with the generating lines perpendicular to the bases, with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius r and length (height) h, then its volume is given by

V = πr2h

and its surface area is:

• the area of the top (πr2) +
• the area of the bottom (πr2) +
• the area of the side (2πrh).

Therefore without the top or bottom (lateral area), the surface area is:

A = 2πrh.

With the top and bottom, the surface area is:

A = 2πr2 + 2πrh = 2πr(r + h).

For a given volume, the cylinder with the smallest surface area has h = 2r. For a given surface area, the cylinder with the largest volume has h = 2r, i.e. the cylinder fits snugly in a cube (height = diameter).