Geometry
Solids
2 +1 = 3. Simple enough. Take any two-dimensional polygon and add one more dimension to it (height), and you have a three-dimensional solid.
A right circular cylinder is just a circle with height. A cube is a square increased upward by the length of one of its sides. A rectangular solid—which most humans would call a box—is a rectangle with height added to it.
There are three main item types associated with three-dimensional figures:
  1. Volume items, designed to blow the minds of students used to area and perimeter
  2. Hidden shape items, like the well-concealed right triangle UPR hiding within the cube
  3. Surface area items, which sometimes throw out the term face
The volume items shouldn’t cause you much trouble. The volume formulas are in the reference portion of the Math test, so check them over if you’re unsure.
The sneaky hidden-shape items are a little tougher but not insurmountable by any means. The box and cube are swarming with triangles, sure, but they are also chock-full of right angles. This means all the triangles are right triangles, so you can use the good ol’ Pythagorean Theorem.
If the box in our diagram were somehow alive, the surface area would be its skin. The surface area of a rectangular solid equals the sum of the area of the six rectangles that make up its sides. For a cube, the surface area would be the sum of the area of its six sides. These sides are sometimes referred to as faces. Written in geometry language:
Surface area of a rectangular solid= 2(length)(width) + 2(length)(height) + 2(height)(width)
Surface area of a cube =
There are formulas for figuring out the surface area of other solids, but the SAT will only ask you to calculate the surface area of a rectangular solid or a cube.
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