Table of COntents
Introduction – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 3
Format of Books – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 4
Suggestions for Use – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 7
Annotated Answer Key and Extension Activities – – – – – – – – – – – 9
Reproducible Tool Set – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 173
ISBN 978-0-8454-8878-2
Copyright © 2016 The Continental Press, Inc.
Excepting the designated reproducible blackline masters, no part of this publication may be reproduced
in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without
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20 Surface Area of Spheres
Pages
173 and 174
Objective
To find the surface area of spheres using the formula
PAR
T
1 Introduction
Introduction
Discuss the formula for the surface area of spheres. Be
sure that students understand each part of the formula.
Work through the example and explain to students
that they can write the surface area in terms of p or
calculate using one of the approximations for p.
Think About It
Students should identify a real-life situation requiring
the surface area of a sphere, such as covering a ball
with decorative paper or measuring to find if a certain
ball is up to regulation for a given sport.
SA 5 4pr 2
surface area
radius
113 5 4(3.14)(r 2)
113 5 12.46r 2 , 9 5 r 2
finding the square root
3 in.
Indiana Academic Standard
multiply by 2
6 in.
8.GM.2 Solve real-world and other mathematical
problems involving volume of cones, spheres, and
pyramids and surface area of spheres.
Vocabulary
surface area: the sum of the areas of each side of
an object
102
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5 ft
1
314 sq ft
​ 
2  ​ 
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PAGES
175 AND 176
LESSON
20 Surface Area of Spheres
PAR
T
Divide the surface area of the sphere by 2.
157 sq ft
no
circle
78.5 sq ft
235.5 sq ft
6,079.04 sq mm
8m
2 Focused
Instruction
Focused
Instruction
First, students will use the surface area formula to
find the radius or the diameter of a sphere. When the
surface area is known, the formula can be solved for
the radius. Knowing the radius allows you to calculate
the diameter as well.
Next, students will use the surface area formula
to find the surface area of a tent in the shape of a
hemisphere. They should recognize how they can
divide the surface area in half and calculate the area of
the circular base to find the total surface area.
Conclude the Focused Instruction section by having
students answer two questions about surface area.
PAR
T
1,256 5 4(3.14)r 2
1,256 5 12.56r 2
100 5 r 2
¯¯ 5 r 5 10
​√100​
Practice
Guided
Practice
3 Guided
Students should complete the Guided Practice section
on their own. Offer assistance as needed, pointing out
the reminder and hint boxes along the right side of
the page.
10
144p
4
288p
or 904.32
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Connections to Process Standards
for Mathematics
• Make sense of problems and persevere in
solving them.
• Model with mathematics.
• Use appropriate tools strategically.
• Attend to precision.
• Look for and make use of structure.
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LESSON
20 Surface Area of Spheres
PAGE
177
PAR
T
Practice
I ndependent
Practice
4 Independent
Answer Rationales
1
Use the formula for the surface area of a sphere and
substitute 25 for r and the approximate value of 3.14
for p. Square 25 and then multiply it by 4 and 3.14:
SA 5 4(3.15)(252) 5 4(3.14)(625) 5 7,850 square
millimeters.
SA 5 4(3.14)(25 2)
5 4(3.14)(625)
5 7,850
7,850
DOK 3
8.GM.2
2
Part A Since the diameter is 18 feet, the radius
of this sphere is 9 feet. Use this measurement to
calculate the surface area in terms of p: SA 5
4p(92); SA 5 4p(81); SA 5 324p square feet.
Part B Multiply the surface area from Part A by 3
to find the surface area of the second sphere: 3 3
324p 5 972p square feet. Then solve the surface
area formula for the radius: 972p 5 4p(r 2); 243 5
¯¯ 5 r  15.6. Multiply the radius by 2 to find
r 2; ​√243​
the diameter: 2 3 15.6 5 31.2 feet.
Part C Divide the surface area of the second
sphere by 2 to find the surface area of the third
sphere: 972p 4 2 5 486p square feet. Then solve
the surface area formula for the radius: 486p 5
¯¯ 
121.5​
5 r. Since √
​ ¯¯
121​ is 11, ​
4pr 2; 121.5 5 r 2; ​√ ¯
¯¯¯ 
is very close to 11, so the approximate
√ 121.5​
radius is 11 feet.
DOK 2
8.GM.2
324p
31.2
11
Extension Activity
Bring in a variety of balls in different sizes. Have
students measure the circumference of the balls and
use that to calculate the radius and the surface area
of each ball.
104
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PAGEs
178 and 179
LESSON
DOK 2
8.GM.2
DOK 3
8.GM.2
Ball 1: r 5 3, SA 5 4p(32) 5 36p
Ball 2: r 5 3.5, SA 5 4p(3.5 2) 5 49p
Ball 3: r 5 4, SA 5 4p(4 2) 5 64p
Ball 4: r 5 4.5, SA 5 4p(4.52) 5 81p
Ball 5: r 5 5, SA 5 4p(5 2) 5 100p
Total SA 5 36p 1 49p 1 64p 1 81p 1 100p 5 330p
330p
DOK 1
8.GM.2
20 Surface Area of Spheres
3
To find the surface area of each sphere, divide the
total surface area by 3: 1,860 4 3 5 620 square
inches. Use this surface area to solve for the length
of the radius: 620 5 4(3.14)r 2; 620 5 12.56r 2;
¯¯ 
 7. So the length of each radius
49.3 5 r 2; ​√49.3​
is about 7 inches.
4
The radius of the smallest ball is 3 centimeters, so its
diameter is 6 centimeters. Since each ball’s diameter
increases by 1 centimeter, the other balls have
diameters of 7, 8, 9, and 10 centimeters. Find the
radius for each by dividing the diameter in half and
then calculate the surface area using the surface area
formula. Leave the answers in terms of p for more
manageable numbers. The surface areas are: Ball 1,
36p sq cm; Ball 2, 49p sq cm; Ball 3, 64p sq cm;
Ball 4, 81p sq cm; Ball 5, 100p sq cm. Add to find
the total surface area: 330p square centimeters.
5
Choice B is correct. The diameter is 52 inches, so the
radius is 26 inches. The surface area is 4p(262) 5
2,704p square inches. In choice B, the diameter was
used instead of the radius to calculate the surface
area. In choice C, the radius was squared, but it
was not multiplied by 4. In choice D, the radius was
multiplied by 2 instead of squared.
r 5 550 4 2 5 275
SA 5 4p(275 2)
5 4p(75,625)
5 302,500p
302,500 4 2 5 151,250
DOK 2
8.GM.2
6
The radius is half the diameter, or 275 yards.
Use this to solve for the surface area of a sphere
with this radius using the surface area formula:
SA 5 4p(2752) 5 302,500p. The surface area of
the hemisphere is half of the total surface area:
302,500p 4 2 5 151,250p square yards.
151,250p
or 474,925
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