Explanation:
A sphere (from Greek σφαῖρα-sphaira,
"globe, ball") is a perfectly round geometrical object in three-dimensional space, such as the
shape of a round ball. Like a circle in two dimensions, a perfect sphere is
completely symmetrical around its center, with all points on
the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The maximum straight
distance through the sphere is known as the diameter of the sphere. It passes through the
center and is thus twice the radius.
In higher mathematics, a careful distinction is made between the
sphere (a two-dimensional spherical surface embedded in three-dimensional Euclidean space)
and the ball (the three-dimensional shape
consisting of a sphere and its interior).
Volume of a sphere
Circumscribed
cylinder to a sphere
In 3 dimensions, the volume inside a sphere (that is, the volume
of a ball) is given by the
formula
where r is the radius of the sphere and π
is the constant pi. This formula
was first derived by Archimedes,
who showed that the volume of a sphere is 2/3 that of a circumscribed cylinder.(Our solved example in
mathguru.com uses this concept).
http://en.wikipedia.org/wiki/Sphere
Cylinder (geometry)
A right
circular cylinder
A cylinder is one of the most basic curvilinear
geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by
this surface and by two planes perpendicular to the axis is also called a
cylinder. The surface area and
the volume of a cylinder have been known since
deep antiquity.
In differential
geometry, a cylinder is defined more broadly as any ruled surface spanned by a one-parameter family of
parallel lines. A cylinder whose cross
section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder respectively.
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 =
πr^{2}h (Our solved example in mathguru.com uses this concept).
http://en.wikipedia.org/wiki/Cylinder_(geometry)
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative
Commons Attribution- ShareAlike 3.0 Unported License.