Lesson 8-4 A Lesson 8-4 A Surface Area of Surface Area of

SpheresSpheres

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.

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

How do you solve problems involving the surface area of a

sphere?

EXAMPLE 1

A solid sphere has a radius of 3m.

Calculate its surface area. (Take p = 22/7)

Surface area = 4 pr² = 4 x 22/7 x 3 x 3

= 113m²

EXAMPLE 2

Find the radius of a sphere with a

Surface area of 64pm²

Surface area = 4 pr²

64p = 4pr²

16 = r² r=square root of 16

r = 4 cm

The radius is 4cm.