The document introduces the formula for calculating the surface area of a sphere. It states that the surface area of a sphere is equal to 4πr^2, where r is the radius of the sphere. The document provides two examples of using the formula to calculate the surface area of a sphere given the radius, or to find the radius given the surface area.

1. Lesson 8-4 A Surface Area of Spheres

2. INTRODUCTION Archimedes, a Greek mathematician, found out that the surface area of a sphere is the same as the curved surface area of a cylinder having the same diameter as the sphere and a height same length as the diameter. Curved surface area of cylinder = 2prh = 2pr(2r) = 4pr2 Thus the surface area of a sphere with radius r = 4 pr2 NOTE: The value of p can never be known exactly, so surface areas of spheres cannot be calculated exactly. Common approximations for p are: 3.14, and 22/7 .

3. Sphere Facts Notice these interesting things: It is perfectly symmetrical It has no edges or vertices It is not a polyhedron All points on the surface are the same distance from the center Sphere Radius Surface Area = 4 × π × r2 Volume = (4/3) × π × r3

4. How do you solve problems involving the surface area of a sphere?

5. EXAMPLE 1 A solid sphere has a radius of 3m. Calculate its surface area. (Take p = 22/7) Surface area = 4 pr ² = 4 x 22/7 x 3 x 3

6. = 113m ²

7. EXAMPLE 2 Find the radius of a sphere with a Surface area of 64pm ² Surface area = 4 pr ²

8. 64p = 4pr ²

9. 16 = r ² r=square root of 16

10. r = 4 cm

11. The radius is 4cm.