## SAT SUBJECT TEST MATH LEVEL 1

## SOLID AND COORDINATE GEOMETRY

**CHAPTER 12 ****Solid Geometry**

**SPHERES**

A sphere is the set of all points in space that are a fixed distance, *r*, from a given point, *O*. *O* is called the center of the sphere, and *r* is the radius.

The two formulas about spheres that you might need to use on the Math 1 test are those for volume and surface area. These two formulas, which are given to you in the “Reference Information” box, constitute the next KEY FACT.

**Key Fact K8**

• **The formula for the volume of a sphere of radius r is** .

• **The formula for the surface area of a sphere of radius r is A** =

**4**π

*r*

^{2}**.**

**Remember**

The formulas in KEY FACT K8 are listed in the Reference Information box on the first page of every Math 1 test.

**EXAMPLE 7:** What is the radius of a sphere whose surface area is equal to the surface area of a cube whose edges are 1?

By KEY FACT K2, the surface area of the cube is 6*e*^{2 }= 6(1)^{2 }= 6. Then by KEY FACT K8,