WARMUPS

1
WARMUPS

• THE STREETS OF MARYS TOWN FORM A RIGHT TRIANGLE.
  IF ONE LEG IS 8 KM LONG, ANOTHER LEG IS 6 KM
  LONG. WHAT IS THE DISTANCE OF THE LONGER STREET?
• THE AVERAGE ANNUAL SNOWFALL IN KODY, WYOMING IS
  26 INCHES. THIS WAS THE AVERAGE ANNUAL SNOWFALL
  FOR 36 CONSECUTIVE YEARS. WHAT IS THE TOTAL
  SNOWFALL IN INCHES FOR THESE 36 YEARS?
• DRAW A CHICKEN

2
Space Figures
PRE-ALGEBRA LESSON 10-4
Pages 541543 Exercises
12. cube 13. pyramid 14. triangular
prism 15. cone 16. a. rectangular
prism b. cone c. sphere 17.
1. The base is a circle. The figure is a
cone. 2. The bases are triangles. The figure is
a triangular prism. 3. The bases are pentagons.
The figure is a pentagonal prism. 4. The base
is a rectangle. The figure is a rectangular
pyramid.
5. The base is a hexagon. The figure is a
hexagonal pyramid. 6. There are no bases. The
figure is a sphere. 7. square
prism 8. triangular pyramid 9. triangular
prism 10. square pyramid 11. rectangular prism
10-4
3
Space Figures
PRE-ALGEBRA LESSON 10-4
18. Check students work. 19. Figures A and C
will not form a cube because bases need to be
on both ends of the vertical faces. 20. square
prism 21. C 22. A 23. B
24. Answers may vary. Sample A net for a
rectangular prism has two rectangular bases
with four rectangular faces attached. A net for
a rectangular pyramid has one rectangular base
with four triangular faces attached.
25.
10-4
4
Space Figures
PRE-ALGEBRA LESSON 10-4
26. Check students work. 27. a. b.
28. B
29. I 30. A 31. H 32. C 33. 2 1
correct drawing, but incorrect or no
labels
10-4
5
Space Figures
PRE-ALGEBRA LESSON 10-4
34. 6.25 m2 20 m2 35. 0.01 m2
0.0314 m2 36. 100 m2 314 m2 37. 9
turns 38. y 3x 6 39. y x 5 40. y
3x 2
10-4
6
Space Figures
PRE-ALGEBRA LESSON 10-4
Describe the base(s) and name each
solid. 1. 2. 3. Name the solid you
can form from this net.
circular base cone
triangular bases triangular prism
octagonal pyramid
10-4
7
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
(For help, go to Lesson 9-6.)
Find the circumference of each circle with the
given radius or diameter. 1. r 5 in. 2. r
4.2 cm 3. d 8 ft 4. d 6.8 in.
10-5
8
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Solutions 1. C 2 r 2. C 2 r C
2(3.14)(5 in.) C 2(3.14)(4.2 cm) C 31.4
in. C 26.4 cm 3. C d 4. C d C
(3.14)(8 ft) C (3.14)(6.8 in.) C 25.1
ft C 21.3 in.
10-5
9
SURFACE AREA OF PRISMS

• CHAPTER 14-2

10
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of the rectangular prism
using a net.
Draw and label a net.
60 60 150 90 150 90 600 Add the
areas.
The surface area is 600 cm2.
10-5
11
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of the rectangular prism.
Step 2 Find the surface area. S.A. L.A. 2B
440 2(5 6) L.A. 440 and B
5 6 440 60 500
The surface area of the rectangular prism is 500
in.2.
10-5
12
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of the cylindrical water
tank.
The surface area of the water tank is about 1,156
ft2.
10-5
13
SURFACE AREA OF A PRISM - WHAT IS IT?

• THE SURFACE AREA OF A PRISM IS THE SUM OF THE
  AREAS OF THE BASES AND ALL FACES OF THE PRISM.
• SURFACE AREA IS EXPRESSED IN SQUARE UNITS.

14
REMEMBER THIS

• FIND THE SURFACE AREA OF THE RECTANGULAR PRISM?

15

• FIND THE SURFACE AREA OF THE RECTANGULAR PRISM?
• 1. FIND THE AREA OF BOTH BASES (THE TOP ONE AND
  THE BOTTOM)

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SURFACE AREA OF RECTANGULAR PRISM
8 IN
10 IN
14 IN
17
SURFACE AREA OF RECTANGULAR PRISM
8 IN
10 IN
14 IN
664 IN 2
18
SURFACE AREA OF TRIANGULAR PRISM
3 FT
8 FT
4 FT
19
SURFACE AREA OF TRIANGULAR PRISM
3 FT
8 FT
108 FT SQ
4 FT
20
SURFACE AREA OF CUBE
4 FT
4 FT
4 FT
21
SURFACE AREA OF CUBE
4 FT
4 FT
4 FT
96 FT SQ
22
SURFACE AREA OF CYLINDERS
23
SURFACE AREA OF CYLINDER
CIRCLE
24
SURFACE AREA OF CYLINDER
CIRCLE
CIRCLE
25
SURFACE AREA OF CYLINDER
CIRCLE
RECTANGLE
CIRCLE
26
SURFACE AREA OF CYLINDER
CIRCLE
27
SURFACE AREA OF CYLINDER
CIRCLE
RECTANGLE
28
SURFACE AREA OF CYLINDER
CIRCLE
RECTANGLE
CIRCLE
29
SURFACE AREA OF CYLINDER
TOTAL AREA 2 x 3.14 x R2

• FIND THE SURFACE AREA OF
• THE TOP CIRCLE
• A 3.14 x R2
• FIND THE SURFACE AREA OF THE BOTTOM CIRCLE
• A 3.14 x R2

30
SURFACE AREA OF CYLINDER

• FIND THE SURFACE AREA OF
• THE MIDDLE
• A 2 x 3.14 x R x H

31
FIND THE AREA OF A THIS CYLINDER
7 CM
30 CM
32
FIND THE AREA OF A THIS CYLINDER
7 CM
FIND AREA OF END A 3.14 x R2 A 3.14 x
72 A 3.14 x 49 A 153.86 CM2
33
FIND THE AREA OF A THIS CYLINDER
7 CM
FIND AREA OF END A 3.14 x R2 A 3.14 x
72 A 3.14 x 49 A 153.86 CM2
34
FIND THE AREA OF A THIS CYLINDER
7 CM
END AREA 2 TIMES 153.86 CM2 BOTH ENDS ARE
307.72 CM2
35
FIND THE AREA OF A THIS CYLINDER
7 CM
30 CM
MIDDLE AREA 2 x 3.14 x r x H MIDDLE AREA 2 x
3.14 x 7 x 30 MIDDLE AREA 1318.8 CM2
36
FIND THE AREA OF A THIS CYLINDER
7 CM
30 CM
MIDDLE AREA 1318.8 CM2 BOTH ENDS
307.72 CM2 TOTAL AREA 1626.52 CM2
37
SURFACE AREA OF CYLINDER
6 FT
20 FT
38
SURFACE AREA OF CYLINDER
6 FT
20 FT
434 FT SQ
39
4 STEP PROBLEM SOLVING

• READ WRITE THE PROBLEM
• ANALYZE THE PROBLEM
• SOLVE THE PROBLEM
• CHECK YOUR ANSWER

40
HOMEWORK

• PAGE 548 EXERCISE DO 1 TO 12.

41
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Pages 548550 Exercises
1. 1,008 m2 2. 3,660 in.2 3. a. b. 206
in.2 c. 1,854 in.2
3. (continued) d. The surface area of the
larger prism is 9 times the surface area of
the smaller prism. 4. 1,056 mm2 5. 11,988
in.2 6. 96 in.2 7. 408 cm2 8. 108 cm2
9. 168 in.2 10. 105.5 m2 11. 175.8
cm2 12. 602.9 yd2 13. 904 cm2 14. 15. 518
m2 16. 5,024 ft2
10-5
42
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
17. 10,800 in.2 18. about 1,130.4 cm2 19. a. 5
sides b. 3,600 ft2 c. 600 20. Answers may
vary. Sample The student thought that you can
interchange diameter and height and have the same
surface areas.
21. Answers may vary. Sample When you paint a
room, you need to find the surface area of the
walls to buy the correct amount of
paint. 22. The height of the base is the height
of the triangular base, but the height of the
prism is the length of a segment perpendicular
to the two bases.
23. The first box requires 399.25 in.2 of
cardboard. The second requires 439.75 in.2 of
cardboard. So the second box requires more
cardboard. 24. a. 6 square units 24 square
units 54 square units b. It is
quadrupled. c. It increases by a factor of
nine. 25. 658 ft2
10-5
43
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
26. Doubling the radius has a greater effect on
the surface area. Doubling the radius or the
height results in the same change in lateral
area, but doubling the radius also increases the
base area. 27. A 28. F 29. B
30. I 31. hexagonal prism 32. pentagonal
pyramid 33. cone 34.
35. 36. 37. 2 teaspoons
10-5
44
Surface Area Prisms and Cylinders
PRE-ALGEBRA LESSON 10-5
Find the surface area of each figure rounded to
the nearest whole unit. 1. triangular prism
with base perimeter 24 cm, base area 24 cm2, and
height 15 cm 2. rectangular prism with base
perimeter 30 cm, base area 50 cm2, and height
150 cm 3. cylindrical candle with radius 2
cm and height 16 cm
408 cm2
4,600 cm2
about 226 cm2
10-5
45
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Find the surface area of the square pyramid.
Step 2 S.A. L.A. B
80 52 Lateral area 80 and B
52. 80 25 105
The surface area of the pyramid is 105 m2.
10-6
46
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Find the surface area of the cone.
The surface area of the cone is about 94 m2.
10-6
47
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Earth has an average radius of 3,963 mi. What is
Earths approximate surface area to the nearest
1,000 mi2? Assume that Earth is a sphere.
197,259,434.64 Multiply.
The surface area of Earth is about 197,259,000
mi2.
10-6
48
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Pages 555556 Exercises
1. 540 cm2 2. 396 in.2 3. 1,017 cm2 4. 33
yd2 5. 1,256 cm2 6. 1,256 in.2 7. 105
cm2 8. about 104 ft2
9. about 804 mm2 10. 81 cm2 11. 28
m2 12. 7,065,000 mi2 13. 1,018
in.2 14. Answers may vary. Sample My friend
forgot that the lateral area of the pyramid is
half of the lateral area of the prism. Also, it
is necessary to add the area of the second base
of the prism.
10-6
49
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
10-6
50
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
24. 4 (continued) Add the areas for a total
surface area of about 215 ft2. 3 1
computational error with work shown 2 2
computational errors with work shown 1 correct
answer with no work shown 25. 1,130
in.2 26. 848 cm2 27. 5 months 28. 1, 3, 7,
21 29. 1, 2, 4, 5, 10, 20, 25, 50, 100
30. 1, 5, 25 31. 1, 2, 4, 8, 16, 32
10-6
51
Surface Area Pyramids, Cones, and Spheres
PRE-ALGEBRA LESSON 10-6
Find the surface area of each space figure. Round
to the nearest whole unit. 1. a square pyramid
with base edge 80 m and slant height 100 m
2. a cone with slant height 22 cm and
radius 7 cm 3. a sphere with radius 12 cm
22,400 m2
about 637 cm2
about 1,809 cm2
10-6