video on fractal’s enjoy! [kml_flashembed movie="http://www.youtube.com/v/G_GBwuYuOOs" width="425" height="350" wmode="transparent" /]

SPHERES:    

A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R³) which are at distance r from a fixed point of that space, where r is a positive real number called the radius of the sphere. The fixed point is called the center or centre, and is not part of the sphere itself. The special case of r = 1 is called a unit sphere.

CONES:      

A right circular cone is a cone whose base is a disk and whose vertex lies on the line perpendicular to the base and passing through the center of the base. Such a cone is characterized by the radius of the base and the altitude of the cone, that is, the distance from the vertex to the center of the base. The slant height of such a cone is the length of a straight line drawn from any point on the perimeter of the cone to the vertex. If the radius of the base is R and the altitude of the cone is H, then the slant height is

which can be seen from the Pythagorean Theorem. The surface area of the cone (neglecting the area of the base) is given by

as can be seen by slicing the cone up the side and unrolling into a sector of a circle whose radius is the slant height and whose perimeter is .

CYLINDERS:  

(h is the height of the cylinder, r is the radius of the top) Surface Area = Areas of top and bottom +Area of the side Surface Area = 2(Area of top) + (perimeter of top)* height Surface Area = 2(pi r ²) + (2 pi r)* h In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That’s the top, the bottom, and the paper label that wraps around the middle. You can find the area of the top (or the bottom). That’s the formula for area of a circle (pi r²). Since there is both a top and a bottom, that gets multiplied by two. The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h. Add those two parts together and you have the formula for the surface area of a cylinder. Surface Area = 2(pi r ²) + (2 pi r)* h

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