For solid shapes on the SAT, the questions are usually not very difficult at all. Most deal with volume or surface areas, which are quite easy to find.
Volume
The interior of a 3-dimensional object is known as the interior. The volume of most solids can be found by simply multiplying the area of the base times the height of the object. The volume of a rectangular solid would be l•w•h while the volume of a cube would be s3, and the volume of a cylinder would be πr2h.
Rectangular solids are a type of prism, although there are triangular and hexagonal prisms. A prism is just a solid where the top and bottom are both a shape (like a triangle for example) while the sides are rectangles. Prisms all have the same formula for finding the volume - the height times the area of the base.
Surface Area
Surface area of a solid can be found by simply adding the areas of all the faces of the object. It is important to not forget about the surfaces on the back of the object that cannot be seen on the drawing on the test.
To find the surface area on the SAT of a rectangular solid, it is simply a matter of multiplying the length times the wwidth, the width by the height, and the length times the height Multiplying each of those answer by 2 (for the back sides) and adding all the numbers together will be the surface area.
For the surface area of a cube, since all the sides are the same it can be found much faster. Use the formula 6s2 to find the surface area of a square.
For cylinders, finding the surface area can be a little tricky. Fortunately, the surface area of a cylinder is rarely asked for on the SAT.
Cones, Pyramids and Spheres
Spheres, pyramids and cones do now show up on the SAT that often, but when they do they usually deal with volume.
