Volume
Having a right circular cylinder with a height h units and a base of radius r units with the coordinate axes chosen so that the origin is at the center of one base and the height is measured along the positive x-axis. A plane section at a distance of x units from the origin has an area of A(x) square units where
or
An element of volume, is a right cylinder of base area Awi square units and a thickness of Δix units. Thus if V cubic units is the volume of the right circular cylinder, by Riemann sums,
Using cylindrical coordinates, the volume can be calculated by integration over
Read more about this topic: Cylinder (geometry)
Famous quotes containing the word volume:
“Measured by any standard known to science—by horse-power, calories, volts, mass in any shape,—the tension and vibration and volume and so-called progression of society were full a thousand times greater in 1900 than in 1800;Mthe force had doubled ten times over, and the speed, when measured by electrical standards as in telegraphy, approached infinity, and had annihilated both space and time. No law of material movement applied to it.”
—Henry Brooks Adams (1838–1918)
“To be thoroughly conversant with a Man’s heart, is to take our final lesson in the iron-clasped volume of despair.”
—Edgar Allan Poe (1809–1845)
“Bishop Berkeley destroyed this world in one volume octavo; and nothing remained, after his time, but mind; which experienced a similar fate from the hand of Hume in 1737.”
—Sydney Smith (1771–1845)