Transcript Surface Area and Volume of Spheres

12.6
SURFACE AREA AND VOLUME OF
SPHERES
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
Find the surface area of the sphere.
SOLUTION
S = 4πr2
Formula for surface area of a sphere.
= 4π(82)
Substitute 8 for r.
= 256π
Simplify.
≈ 804.25
Use a calculator.
ANSWER
The surface area of the sphere is about 804.25 square
inches.
GUIDED PRACTICE
2.
for Examples 1 and 2
The surface area of a sphere is 30π square meters.
Find the radius of the sphere.
ANSWER
2.71
EXAMPLE 3 Use 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 the
radius is 12 = 6 feet.
2
EXAMPLE 3 Use the circumference of a sphere
Use the formula for the surface area of a sphere.
S = 4πr2 = 4π(62)= 144π
ANSWER
The surface area of the outer ball is 144π, or about
452.39 square feet.
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 volume
of the sphere as the sum of
n pyramids each with a volume
of V = (1/3)Bh.

EXAMPLE 4 Find the volume of a sphere
The soccer ball has a diameter of 9 inches. Find its
volume.
SOLUTION
The diameter of the ball is 9 inches, so the radius is
9
= 4.5 inches.
2
4
V = 3 πr3
4
= 3 π(4.5)3
Formula for volume of a sphere
Substitute.
EXAMPLE 4
Find the volume of a sphere
= 121.5π
Simplify.
≈ 381.70
Use a calculator.
ANSWER
The volume of the soccer ball is 121.5π, or about 381.70
cubic inches.
EXAMPLE 5
Find the volume of a composite solid
Find the volume of the composite solid.
SOLUTION
1 4 3
( πr )
2 3
= π(2)2(2) – 2 π(2)3
3
2
= 8π –
3
(8π)
= πr2h –
Formulas for volume
Substitute.
Multiply.
EXAMPLE 5
Find the volume of a composite solid
= 24 π – 16 π
3
3
= 8 π
3
Rewrite fractions using least
common denominator.
Simplify.
ANSWER
The volume of the solid is 8 π, or about 8.38 cubic
3
inches.
HOMEWORK

842-843
 3-9
odd, 13,17,21-27