Volumes of Pyramids and Cones
Lesson 11-5
Geometry
Lesson Quiz
Find the volume of each figure. When appropriate, leave your answer in
terms of .
1.
2.
60 ft3
mm3
1470
3. square pyramid with base edges 24 in. long and slant height 15 in. 1728 in.3
4. cone with diameter 3 m and height 4 m 3
m3
5.
150 ft3
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Check Skills You’ll Need
(For help, go to Lesson 1-9.)
Find the area and circumference of a circle with the given radius. Round
your answers to the nearest tenth.
1. 6 in.
2. 5 cm
3. 2.5 ft
4. 1.2 m
5. 15 yd
6. 12 mm
1. A =
r2 =
(6)2 = 36
113.1 in.2, C = 2
r= 2
(6) = 12
37.7 in.
2. A =
r2 =
(5)2 = 25
78.5 cm2, C = 2
r= 2
(5) = 10
31.4 cm
3. A =
r2 =
(2.5)2 = 6.25
19.6 ft2, C = 2
r= 2
(2.5) = 5
4. A =
r2 =
(1.2)2 = 1.44
4.5 m2, C = 2
r= 2
(1.2) = 2.4
5. A =
r2 =
(15)2 = 225
706.9 yd2, C = 2
6. A =
r2 =
(12)2 = 144
452.4 mm2, C = 2
r= 2
r= 2
(15) = 30
(12) = 24
15.7 ft
7.5 m
94.2 yd
75.4 mm
Check Skills You’ll Need
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Notes
A sphere is the set of points in space equidistant
from a given point called the center. A radius of a
sphere is a segment that has one endpoint at the
center and the other endpoint on the sphere. A
diameter is a segment passing through the center
with endpoints on the sphere.
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Notes
A great circle is the intersection of the sphere and a
plane passing through the center of the sphere. The
circumference of a great circle is the circumference
of the sphere. A great circle divides a sphere into two
hemispheres.
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Notes
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Notes
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Additional Examples
Finding Surface Area of a Sphere
Find the surface area of the sphere below. Leave your answer
in terms of .
S.A. = 4
r2
Use the formula for the surface area of a sphere.
• 92
Substitute r = 18 = 9.
=4
= 324
2
Simplify.
The surface area of the sphere is 324
Lesson
Main
Lesson
11-6
ft2.
Quick Check
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Additional Examples
Real-World Connection
Quick Check
The circumference of a rubber ball is 13 cm. Calculate its
surface area to the nearest whole number.
Step 1: Use the circumference to find the radius in terms of .
C=2 r
Use the formula for circumference.
13 = 2
r
Substitute 13 for C.
13
=r
2
Solve for r.
Step 2: Use the radius to find the surface area.
S.A. = 4
=4
r2
Use the formula for the surface area of a sphere.
• ( 13 )2
Substitute 2
Simplify.
= 169
2
53.794371
13
for r.
Use a calculator.
To the nearest whole number, the surface area of the rubber ball is 54 cm2.
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Additional Examples
Finding Volume
Find the volume of the sphere. Leave your answer in
terms of .
V= 4
3
=4
3
r3
Use the formula for the volume of a sphere.
• 153
Substitute r =
= 4500
Simplify.
The volume of the sphere is 4500
Lesson
Main
30
= 15.
2
cm3.
Lesson
11-6
Quick Check
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Additional Examples
Using Volume to Find Surface Area
The volume of a sphere is 1 in.3. Find its surface area to the
nearest tenth.
Step 1: Use the volume to find the radius r.
3
V= 4
3
r3
Use the formula for the volume of a sphere.
1= 4
3
r3
Substitute.
3
= r3
4
Solve for r 3.
3
= r
4
Find the cube root of each side.
r
0.62035049
Lesson
Main
Use a calculator.
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Additional Examples
(continued)
Step 2: Use the radius to find the surface area.
S.A. = 4
4
r2
(0.62035049)2
4.8359744
Use the formula for the surface area of a sphere.
Substitute.
Use a calculator.
To the nearest tenth, the surface area of the sphere is 4.8 in.2.
Quick Check
Lesson
Main
Lesson
11-6
Feature
Surface Areas and Volumes of Spheres
Lesson 11-6
Geometry
Lesson Quiz
For Exercises 1–3, find the surface area. Leave your answer in terms of
1. a sphere whose diameter is 13 cm
2. a ball whose circumference is 19
3. a sphere whose volume is 288
169
cm2
mm 361
in.3
144
.
mm2
in.2
For Exercises 4 and 5, find the volume. Round your answer to the nearest
whole number.
4. sphere with radius 5 m
5. sphere with diameter 7 yd
Lesson
Main
524 m3
180 yd3
Lesson
11-6
Feature
Geometry
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Geometry
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Geometry
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