1. Entry Task

2. Warm Up
Find the perimeter and area of
each polygon.
a rectangle with base 14 cm and height 9 cm
2. a right triangle with 9 cm and 12 cm legs
3. an equilateral triangle with side length 6 cm
P = 46 cm; A = 126 cm2
P = 36 cm; A = 54 cm2

3. Surface Area of Prisms and Cylinders
Learning Target:
I can find the surface area of prisms and cylinders
Success Criteria:
I can apply the surface area to real world problems.

4. Vocabulary
Lateral vs Surface Area
Oblique Prism

5. Group Work As a group find the surface area of the following….. 276cm2

6. Prisms and cylinders have 2 congruent parallel bases.
A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edge of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face. (They are “tipped”)

7. An altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude.
Surface area is the total area of all faces and curved
surfaces of a three-dimensional figure. The lateral
area of a prism is the sum of the areas of the lateral faces.

8. The net of a right prism can be drawn so that the lateral faces form a rectangle with the same height as the prism. The base of the rectangle is equal to the
perimeter of the base of the prism.

9. The surface area of a right rectangular prism with length ℓ, width w, and height h can be written as
S = 2ℓw + 2wh + 2ℓh.
The surface area formula is only true for right prisms. To find the surface area of an oblique prism, add the areas of the faces.
Caution!

10. Example 1A: Finding Lateral Areas and Surface Areas of Prisms
Find the lateral area and surface area of the right rectangular prism. Round to the nearest tenth, if necessary.
L = Ph
P = 2(9) + 2(7) = 32 ft
= 32(14) = 448 ft2
S = Ph + 2B
= (7)(9) = 574 ft2

11. Example 1B: Finding Lateral Areas and Surface Areas of Prisms
Find the lateral area and surface area of a right regular triangular prism with height 20 cm and base edges of length 10 cm. Round to the nearest tenth, if necessary.
L = Ph
= 30(20) = 600 cm2
P = 3(10) = 30 cm
S = Ph + 2B
The base area is

12. Check It Out! Example 1
Find the lateral area and surface area of a cube with edge length 8 cm.
L = Ph
= 32(8) = 256 cm2
P = 4(8) = 32 cm
S = Ph + 2B
= (8)(8) = 384 cm2

13. The lateral surface of a cylinder is the curved surface that connects the two bases. The axis of a cylinder is the segment with endpoints at the centers of the bases. The axis of a right cylinder is perpendicular to its bases. The axis of an oblique cylinder is not perpendicular to its bases. The altitude of a right cylinder is the same length as the axis.

15. Homework p. 704 #7-9,11-19,25,30 Challenge – 40 Remember!
Always round at the last step of the problem. Use the value of  given by the  key on your calculator.
Remember!

16. Example 2A: Finding Lateral Areas and Surface Areas of Right Cylinders
Find the lateral area and surface area of the right cylinder. Give your answers in terms of .
The radius is half the diameter, or 8 in.
L = 2rh = 2(8)(10) = 160 in2
S = L + 2r2 = 160 + 2(8)2
= 288 in2

17. Example 2B: Finding Lateral Areas and Surface Areas of Right Cylinders
Find the lateral area and surface area of a right cylinder with circumference 24 cm and a height equal to half the radius. Give your answers in terms of .
Step 1 Use the circumference to find the radius.
C = 2r
Circumference of a circle
24 = 2r
Substitute 24 for C.
r = 12
Divide both sides by 2.

18. Example 2B Continued
Find the lateral area and surface area of a right cylinder with circumference 24 cm and a height equal to half the radius. Give your answers in terms of .
Step 2 Use the radius to find the lateral area and surface area. The height is half the radius, or 6 cm.
L = 2rh = 2(12)(6) = 144 cm2
Lateral area
S = L + 2r2 = 144 + 2(12)2
= 432 in2
Surface area

19. Check It Out! Example 2
Find the lateral area and surface area of a cylinder with a base area of 49 and a height that is 2 times the radius.
Step 1 Use the circumference to find the radius.
A = r2
Area of a circle
49 = r2
Substitute 49 for A.
Divide both sides by  and take the square root.
r = 7

20. Check It Out! Example 2 Continued
Find the lateral area and surface area of a cylinder with a base area of 49 and a height that is 2 times the radius.
Step 2 Use the radius to find the lateral area and surface area. The height is twice the radius, or 14 cm.
L = 2rh = 2(7)(14)=196 in2
Lateral area
S = L + 2r2 = 196 + 2(7)2 =294 in2
Surface area

21. Example 3: Finding Surface Areas of Composite Three-Dimensional Figures
Find the surface area of the composite figure.

22. Example 3 Continued
The surface area of the rectangular prism is .
A right triangular prism is added to the rectangular prism. The surface area of the triangular prism is .
Two copies of the rectangular prism base are removed. The area of the base is B = 2(4) = 8 cm2.

23. Example 3 Continued
The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure.
S = (rectangular prism surface area) + (triangular prism surface area) – 2(rectangular prism base area)
S = – 2(8) = 72 cm2

24. Check It Out! Example 3
Find the surface area of the composite figure. Round to the nearest tenth.

25. Check It Out! Example 3 Continued
Find the surface area of the composite figure. Round to the nearest tenth.
The surface area of the rectangular prism is
S =Ph + 2B = 26(5) + 2(36) = 202 cm2.
The surface area of the cylinder is
S =Ph + 2B = 2(2)(3) + 2(2)2 = 20 ≈ 62.8 cm2.
The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure.

26. Check It Out! Example 3 Continued
Find the surface area of the composite figure. Round to the nearest tenth.
S = (rectangular surface area) +
(cylinder surface area) – 2(cylinder base area)
S = — 2()(22) = cm2

27. Example 4: Exploring Effects of Changing Dimensions
The edge length of the cube is tripled. Describe the effect on the surface area.

28. Example 4 Continued
24 cm
original dimensions:
edge length tripled:
S = 6ℓ2
S = 6ℓ2
= 6(8)2 = 384 cm2
= 6(24)2 = 3456 cm2
Notice than 3456 = 9(384). If the length, width, and height are tripled, the surface area is multiplied by 32, or 9.

29. Check It Out! Example 4
The height and diameter of the cylinder are
multiplied by . Describe the effect on the
surface area.

30. 11 cm 7 cm Check It Out! Example 4 Continued original dimensions:
height and diameter halved:
S = 2(112) + 2(11)(14)
S = 2(5.52) + 2(5.5)(7)
= 550 cm2
= 137.5 cm2
Notice than 550 = 4(137.5). If the dimensions are halved, the surface area is multiplied by

31. Example 5: Recreation Application
A sporting goods company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon.
Which tent requires less nylon to manufacture?

32. Example 5 Continued
Pup tent:
Tunnel tent:
The tunnel tent requires less nylon.

33. Check It Out! Example 5
A piece of ice shaped like a 5 cm by 5 cm by 1 cm rectangular prism has approximately the same volume as the pieces below. Compare the surface areas. Which will melt faster?
The 5 cm by 5 cm by 1 cm prism has a surface area of 70 cm2, which is greater than the 2 cm by 3 cm by
4 cm prism and about the same as the half cylinder. It will melt at about the same rate as the half cylinder.