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 $V=\frac{4}{3}\pi r^3.$
• The formula for the surface area of a sphere of radius r is A = 4πr².

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 6e² = 6(1)² = 6. Then use KEY FACT K8:

$4\pi r^2=6\Rightarrow r^2=\frac{6}{4\pi }\mathit{\Rightarrow }r=\sqrt{\frac{6}{4\pi }}\mathit{\approx }0.69$