SURFACE AREA AND VOLUME OF SPHERES

12.6

VOCABULARY

Sphere – Set of all point in space equidistant from a given point.

Center Radius – a segment from the center to

a point on the sphere. Chord – A segment whose endpoints

are on the sphere. Diameter – A chord that contain the

center.

VOCAB PICTURES

SURFACE AREA

The surface area S of a sphere is S = 4 πr2 Where r is the radius

EXAMPLE 1 Find the surface area of a sphere

SOLUTION

S = 4πr2

= 4π(82)

= 256π

≈ 804.25

Formula for surface area of a sphere.

Substitute 8 for r.

Simplify.

Use a calculator.

Find the surface area of the sphere.

The surface area of the sphere is about 804.25 squareinches.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

2. The surface area of a sphere is 30π square meters.Find the radius of the sphere.

2.71

ANSWER

EXAMPLE 3Use the circumference of a sphere

EXTREME SPORTS

In a sport called sphereing, a person rolls down a hill inside an inflatable ball surrounded by another ball. The diameter of the outer ball is 12 feet. Find the surface area of the outer ball.

SOLUTION

The diameter of the outer sphere is 12 feet, so theradius is = 6 feet.12

2

EXAMPLE 3Use the circumference of a sphere

Use the formula for the surface area of a sphere.

S = 4πr2= 4π(62)= 144π

The surface area of the outer ball is 144π, or about 452.39 square feet.

ANSWER

VOCAB

Great Circle – a cross section of the sphere that contain the center

Hemisphere – one half of the circle created by the great circle cross section.

VOLUME

Approximate the volumeof the sphere as the sum ofn pyramids each with a volumeof V = (1/3)Bh.

EXAMPLE 4Find the volume of a sphere

SOLUTION

The soccer ball has a diameter of 9 inches. Find its volume.

Formula for volume of a sphere

Substitute.

V = πr343

= π(4.5)3

43

The diameter of the ball is 9 inches, so the radius is

= 4.5 inches.

92

EXAMPLE 4Find the volume of a sphere

= 121.5π

≈ 381.70

Simplify.

Use a calculator.

The volume of the soccer ball is 121.5π, or about 381.70 cubic inches.

ANSWER

EXAMPLE 5Find the volume of a composite solid

SOLUTION

= πr2h – ( πr3)12

43

= π(2)2(2) – π(2)3

23 Substitute.

Formulas for volume

23

= 8π – (8π)

Multiply.

Find the volume of the composite solid.

EXAMPLE 5Find the volume of a composite solid

= π – π

243

163

83=

π

Rewrite fractions using leastcommon denominator.Simplify.

The volume of the solid is π, or about 8.38 cubic inches.

83

ANSWER

HOMEWORK

842-843 3-9 odd, 13,17,21-27