12.6. sphere – set of all point in space equidistant from a given point. center radius – a...
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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
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