1. Surface Area Lateral and Total Surface Area
8.7B

2. Surface Area of Cylinders
Essential Question:
Why are formulas important in math and science?
We will… determine the lateral area and total surface area of cylinders.
I will… solve problems involving the surface area of cylinders.

3. Vocabulary Surface Area- The total area of the surface of a 3D object.
Lateral Area- The sum of the areas of the faces of a figure. (Not including the bases)

4. Vocabulary
Total Surface Area- The sum of the areas of ALL the faces including the bases.

5. Lateral Surface area Formula:
Cylinder S= 2𝝅rh
S= lateral
𝜋 = 3.14
r= radius
h= height

6. Total Surface area Formula:
Lateral Formula
Cylinder S= 2𝝅rh + 2𝝅 𝒓 𝟐
S= lateral/Total surface area
𝜋 = 3.14
r= radius
h= height
Finding the area of BOTH bases.

7. Lateral Area Practice 1:
3 in
Identify the variables
S= 2𝝅rh
r= 3
h=7 𝝅=𝟑.𝟏𝟒
2. Plug in and Solve
S= 2(𝟑.𝟏𝟒)(𝟑)(𝟕)
S= 𝒊𝒏 𝟐
7 in
Base
Base

8. 3. Add lateral & Area of both bases to get total surface area.
Lateral Formula
Base
Base
1. Formula
S= 2𝝅rh + 2𝝅 𝒓 𝟐
2. Plug in and Solve
2𝝅 𝒓 𝟐
2(3.14)( 𝟑 𝟐 )
Area of BOTH bases=56.52
3. Add lateral & Area of both bases to get total surface area.
S= = 𝒊𝒏 𝟐
Finding the area of BOTH bases.
3 in
7 in

9. Total Surface Area:
3. Add lateral & Area of both bases to get total surface area. S= = 𝒊𝒏 𝟐
Lateral
Area of the Bases

10. Surface Area: Rectangular Prisms
8.7B

11. We will use previous knowledge of surface area to make connections to the formulas for lateral and total surface area. I will solve for lateral and surface area of a rectangular prism.

12. What is the lateral area on a rectangular prism? Which are the bases?

13. Formulas: Lateral: S=Ph P= perimeter of the base P=(2 x L) + (2 x w)
h= height
Total Surface area: S= Ph + 2B
B=area of the base. B= L x w

14. Practice 1: Rectangular prism L= 12m W=6m h=7m Find the lateral area:
S=Ph
S= (s+s+s+s)(h)
2. Find the total surface area.
S= Ph+2B

15. Total Surface area: S= Ph + 2B

16. Practice 2: Rectangular prism L=14 ft W= 7ft H=8ft
Find the lateral area:
S=Ph
S= (s+s+s+s)(h)
2. Find the total surface area.
S= Ph+2B

17. Practice 3: Rectangular prism L= 7 cm W= 3 cm H= 3 cm
Find the lateral area:
S=Ph
S= (s+s+s+s)(h)
2. Find the total surface area.
S= Ph+2B

18. Practice 4: Rectangular prism L=4.9 ft W= 3 ft H= 0.7
Find the lateral area:
S=Ph
S= (s+s+s+s)(h)
2. Find the total surface area.
S= Ph+2B

19. Practice 5: Rectangular prism L= 4 m W= 3 m H= 2 m
Find the lateral area:
S=Ph
S= (s+s+s+s)(h)
2. Find the total surface area.
S= Ph+2B

20. Surface Area: Triangular Prism
8.7B

21. Goal
We will determine the lateral area and total surface area of triangular prisms.
I will solve for lateral and surface area of a triangular prism.

22. Essential Question
Why are formulas important in math and science?

23. Vocabulary
Base of a triangular prism- the two congruent, opposite and parallel faces shaped like triangles.
Height of the triangular prism- the length of a side that is perpendicular to both bases.
Perimeter- the distance around a closed plane figure.

24. Triangular Prism .

25. S = Ph + 2B Total Surface Area S=Ph Lateral Surface Area
Formulas
S = Ph + 2B Total Surface Area
S=Ph Lateral Surface Area
P = Perimeter of the base/triangle P=(s+s+s)
h= Height of the prism
B = area of the base B=1/2bh
b= base of the triangle

26. Triangle Lateral Surface Area S= Ph
Solve for Lateral surface area.
S= Ph
S= (s+s+s)(h)
S= ( )(13) S=
S = 624 ft square
h = 12 13 15 18
Dimensions
Triangle:
h= 12
b= 18
Rectangle:
h=13
w= 15

27. Triangle Total surface area S= Ph + 2B
Solve for Total surface area.
S= Ph + 2B
S= (s+s+s)(h) (1/2bh)
S= (
h = 12 13 15 18
Dimensions
Triangle: h= b=
Rectangle: w=

28. Triangle Lateral surface area P= Ph
1. Solve for lateral surface area.

29. Triangle Lateral surface area P= Ph + 2B
1. Solve for lateral surface area.

30. Triangle Lateral surface area P= Ph
1. Solve for lateral surface area.

31. Triangle Lateral surface area P= Ph + 2B
1. Solve for lateral surface area.

32. Triangle Lateral surface area P= Ph
1. Solve for lateral surface area.

33. Triangle Lateral surface area P= Ph + 2B
1. Solve for lateral surface area.