SATII数学考试快递——Relating Length, Surface Area, and Volume
The Math IC tests not only whether you’ve memorized the formulas for the different geometric solids, but also whether you understand those formulas. The test gauges your understanding by asking you to calculate the lengths, surface areas, and volumes of various solids. The Math IC will ask you about the relationship between these three properties. The Math IC includes two kinds of questions covering these relationships.
Comparing Dimensions
The first way the Math IC will test your understanding of the relationship among the basic measurements of geometric solids is by giving you the length, surface area, or volume of different solids and asking you to compare their dimensions. The math needed to answer comparing-dimensions questions isn’t that hard. But in order to do the math, you need to have a good grasp of the formulas for each type of solid and be able to relate those formulas to one another algebraically. For example,
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This question tells you that the surface area of a sphere and the volume a cylinder are equal. A sphere’s surface area is 4π(rs)2, where rs is the radius of the sphere.
A cylinder’s volume is π(rc)2 
h, where rc is the radius of the cylinder, and h is its height. Therefore,
The question asks for the ratio between the radii of the sphere and the cylinder. This ratio is given by r s/rc. Now you can solve the equation 4πrs2 = πrc2 
h for the ratio rs/rc.
Changing Measurements
The second way the Math IC will test your understanding of the relationships among length, surface area, and volume is by changing one of these measurements by a given factor, and then asking how this change will influence the other measurements.