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Pre-Algebra: Chapter 12-5
Surface Area: Prisms and Cylinders
Prisms, be they rectilinear (rectangular) or triangular (triangles) have sides, called “faces” and points, called “vertices” and “edges”. You can figure out the “SURFACE AREA” of a prism by taking the sides apart one at a time and treating them as either rectangles or triangles. Remembering the formulas for area of a rectangle as `Area=l*w` and the area of a triange as `Area = (1/2)(b*h)` can give you all the tools you need to find the surface area.
For cylinders, its a little different. The end caps are easy, they are just the area of the disk or circle. The area of a circle is `Area=2pir^2` or `Area=pid` because `2r=d`. For the side of the cylinder, just “unroll” the tube. The circumference of the end caps, is the length of the rectangle formed during the unrolling of the tube. Remember, circumference, `C=2pir`
If you can visualize, or take apart the prism or cylinder, those pieces layed out on the floor are called a `NET`. The surface area of the object becomes the surface area of the `NET`.
Here is a link to purplemath.com with the formulas laid out nice and neat.
Algebra: Chapter 12-7
Joint and Combined Variation
Joint variation is written in the form `z=k*x*y`, where `k` is the CONSTANT OF VARIATION and BOTH `x` and `y` vary directly as `z`. So, when `z` goes up in value, so do `x` and `y`.
In combined variation, one of the variables is inversely related, while the other is directly related. The Combined varation looks like `z=(k*x)/y` As `z` goes up , so does `x` but `y` goes down.