1. Saxon Math:
Course 3
Lesson #85 : Surface Area of Prisms & Cylinders

2. “Do Now”
• Read Saxon Math Book pages 568 - 570
• Define: (Write the bolded definitions in your own words)
1. Surface Area
2. Lateral Surface Area
3. Cylinder
4. Prism
2. Answer the following Questions
1. What is the formula for the lateral surface area of a prism
and cylinder?
2. What do you need to add to the lateral surface area to
make it the total surface area?
3. How do you find the area of a triangle?
4. How do you find the area of a circle?
5. How do you find the area of a rectangle?

3. Homework
• SMB Lesson 85
• Ask Leyonne :)
• 1, 2, 4, 7, 8, 16, 20 - 25
• Study Surface Area of Prisms & Cylinders

4. Homework Questions
Lesson 111

5. Homework Questions
Lesson 111

6. Agenda
Pre-Reading --- 8 minutes
HW Questions --- 8 minutes
Expectations --- 3 minutes
Worksheet --- 18 minutes
S.A. of Prisms & Cylinders --- 20 minutes
S.A. of Spheres --- 10 minutes
Study Check --- 15 minutes

7. Class Expectations
• Taking Notes
• Write Everything that is in RED
• Clipboard Checks
• Sentence Detention

8. Worksheet Time
• You guys can teach yourselves at this point
• If you need help, ask those at your table
FIRST
• Everyone at each table should be working
together
• You may sit across from each other

9. Worksheet Time
• Raise your hand and let me know when
you finish!

10. Lesson 85: Surface Area
of Prisms & Cylinders
• Lesson Objectives:
1. I will be able to calculate the surface
areas and lateral surface area of cylinders
and prisms

11. Lesson Agenda
Lateral Surface Area --- 8 minutes
Total Surface Area --- 12 minutes

12. Lateral Surface Area
• Lateral Surface Area - area of the SIDES/
WALLS of a Prism or Cylinder
• Lateral surface area is just like stretching the
perimeter of the base

13. Lateral Surface Area
• Lateral Surface Area - area of the SIDES/
WALLS of a Prism or Cylinder
• Lateral surface area is just like stretching the
perimeter of the base

14. Lateral Surface Area
• Lateral Surface Area - area of the SIDES/
WALLS of a Prism or Cylinder
• Lateral surface area is just like stretching the
perimeter of the base

15. Lateral Surface Area
• Lateral Surface Area - area of the SIDES/
WALLS of a Prism or Cylinder
• Lateral surface area is just like stretching the
perimeter of the base

16. Lateral Surface Area
• Lateral Surface Area - area of the SIDES/
WALLS of a Prism or Cylinder
• Lateral surface area is just like stretching the
perimeter of the base

17. Lateral Surface Area

18. Lateral Surface Area
• Step #1: Identify Base (How do we do this?)

19. Lateral Surface Area
• Step #1: Identify Base (How do we do this?)
• Step #2: Find perimeter of Base

20. Lateral Surface Area
• Step #1: Identify Base (How do we do this?)
• Step #2: Find perimeter of Base
• Step #3: Multiply perimeter of Base by
Height

21. Lateral Surface Area
• Step #1: Identify Base (How do we do this?)
• Step #2: Find perimeter of Base
• Step #3: Multiply perimeter of Base by
Height
LSA = (Perimeter of Base) × height

22. Lateral Surface Area
(Example)
• Mr. D has a big cylindrical silo in his
backyard that is shown below. He wants to
paint the walls of his silo red. If his silo has
a width of 12 meters, and a height 20
meters.
20 m
12 m

23. Lateral Surface Area
(Example)
• Mr. D has a big cylindrical silo in his
backyard that is shown below. He wants to
paint the walls of his silo red. If his silo has
a width of 12 meters, and a height 20
meters.
20 m
12 m

24. Lateral Surface Area
(Group Practice)
• Find the lateral surface area of the following shapes
4 ft
4 ft 3 ft 12 ft
8 ft 6 ft
5 ft
• Mr. D’s classroom is in the shape of a pentagonal prism. If he
wants to paint all the sides except for the front and back of
the room. Find the area of the room that he needs to paint.
5 yd
5 yd
3 yd
3 yd
15 yd
12 yd
• If one can of paint covers 200 sq. ft. Determine how many
cans of paint Mr. D needs.

25. Lateral Surface Area
(Answers)
• 104 ft2
• 144(pi) ft 2
• 420 yd 2
• 3 cans of paint

26. Total Surface Area

27. Total Surface Area
• Step #1: Find Lateral Surface Area (LSA)

28. Total Surface Area
• Step #1: Find Lateral Surface Area (LSA)
• Step #2: Find area of bases

29. Total Surface Area
• Step #1: Find Lateral Surface Area (LSA)
• Step #2: Find area of bases
• Step #3: Add area of bases and LSA

30. Total Surface Area
• Step #1: Find Lateral Surface Area (LSA)
• Step #2: Find area of bases
• Step #3: Add area of bases and LSA
TSA = LSA + (Area of Bases)

31. Total Surface Area
• Step #1: Find Lateral Surface Area (LSA)
• Step #2: Find area of bases
• Step #3: Add area of bases and LSA
TSA = LSA + (Area of Bases)
TSA = LSA + 2B

32. Total Surface Area
(Examples)
8m
6m 8m
10 m
12 m

33. Total Surface Area
(Examples)
• Find the Total Surface Area of the following
shape
8m
6m 8m
10 m
12 m

34. Total Surface Area
(Examples)
• Find the Total Surface Area of the following
shape
8m
6m 8m
10 m
12 m
• A can of soup has a diameter of 6 cm and a
height of 14 cm. What is the total surface
area of the can of soup?

35. Total Surface Area
(Group Practice)
• SMB p. 570
• a-e

36. Total Surface Area
(Answers)
• 345.4 cm2
• 288 in
2
• 188.4 cm 2
• 240 in
2
• 3768 ft 2

37. Surface Area of a
Sphere
• Same as lateral surface area of a cylinder
with the same height and diameter!
LSA = (Perimeter of Base) × height
6 mm
3 mm
3 mm

38. Surface Area of a
Sphere
• Deriving the formula for Surface Area of a
Sphere
LSA of Cylinder = π d × height
8 in
4 in

39. Surface Area of a
Sphere
2
SA of Sphere = 4π r

40. Surface Area of a
Sphere (Example)
• Find the surface area of a sphere with
diameter of 4.2 inches
• If a tennis ball has a surface area of 48π
square inches, what is the radius of the ball?

41. Group Practice
• Find the surface area of a sphere with
diameter of 7.5 meters
• Mr. D wants to give Mr. Magic a volleyball as
a gift. If it takes Mr. D exactly 324 square
inches of wrapping paper to cover the
volleyball, what is the diameter of the ball?

42. Group Practice
• SMB p. 734
• a-d

43. Study Check
• Lesson #111 - Volume & Surface Area of
Spheres