Page 56 - Math Course 3 (Book 2)

Geometric Surface Area: Spheres
Mo. 8

Lesson 4 Key Concept

KEY CONCEPTS: Surface Area of a Sphere

1. Recognize and define basic properties of If a sphere has a surface are of T
spheres.
2. Find surface areas of spheres. square units and a radius of r r
units, then T = 4 r².

MO. 8 - L4a

Finding Surface Areas of
Spheres

Let’s Begin

Vocabulary A-Z

Let us learn some vocabulary
Spheres and Circles

great circle Example
The intersection of a plane and a sphere can be a
point or a circle. When a plane intersects a sphere
so that it contains the center of the sphere, the In the figure, O is the center of the sphere, and
intersection is called a great circle. plane P intersects the sphere in circle R. If OR = 6
centimeters and OS = 14 centimeters, find RS.

a point a circle a great circle

hemisphere
Each great circle separates a sphere into two con-
gruent halves, each called a hemisphere. Note that
a hemisphere has a circular base.
The radius of circle R is segment RS and S is a point
on circle R and on sphere O. Use the Pythagorean
Theorem for right triangle ORS to solve for RS.

OS² = RS² + OR² Pythagorean Theorem

14² = RS² + 6² OS = 14, OR = 6
196² = RS² + 36 Simplify.

160 = RS² Subtract 36 from each side.

Hemisphere 12.6 ≈ RS Use a calculator.

great circles RS is approximately 12.6
Answer
centimeters.

48