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:
“Legends of prediction are common throughout the whole Household of Man. Gods speak, spirits speak, computers speak. Oracular ambiguity or statistical probability provides loopholes, and discrepancies are expunged by Faith.”
—Ursula K. Le Guin (b. 1929)
“When we consider what, to use the words of the catechism, is the chief end of man, and what are the true necessaries and means of life, it appears as if men had deliberately chosen the common mode of living because they preferred it to any other. Yet they honestly think there is no choice left. But alert and healthy natures remember that the sun rose clear. It is never too late to give up our prejudices.”
—Henry David Thoreau (1817–1862)