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).
Read more about this topic: Cylinder (geometry)
Famous quotes containing the word common:
“The peace of God, which passeth all understanding.”
—Bible: New Testament St. Paul, in Philippians, 4:7.
The words are also used in the Book of Common Prayer, Holy Communion (1662)
“All the philosophy, therefore, in the world, and all the religion, which is nothing but a species of philosophy, will never be able to carry us beyond the usual course of experience, or give us measures of conduct and behaviour different from those which are furnished by reflections on common life. No new fact can ever be inferred from the religious hypothesis; no event foreseen or foretold; no reward or punishment expected or dreaded, beyond what is already known by practice and observation.”
—David Hume (1711–1776)