1. Surface Area

2. How much cardboard does it take to make a cereal box?
Surface Area of Rectangular Prisms
Have you ever wondered?
How much cardboard does it take to make a cereal box?

3. Surface Area- the sum of the areas of all the faces

4. What are the dimensions of this rectangle?
Do you see the RED face?
What are the dimensions of this rectangle?
4 in.
10 in.

5. Do you see another face that is just like the RED face?
Where is it located?

6. Yes, it’s on the back.
10 in.
4 in.

7. 40 in2
Now there are 2 rectangles
that each have an area of 40 sq. in.

8. What are the dimensions of this rectangle?
Do you see the BLUE face?
What are the dimensions of this rectangle?
4 in.
7 in.

9. Do you see another face that is just like the BLUE face?
Where is it located?

10. Yes, it’s on the left side.
7 in.
4 in.
4 in.
7 in.

11. 28 in2
Now there are 2 rectangles
that each have an area of 28 sq. in.

12. Do you see the GREEN face?
What are the dimensions of this rectangle?
7 in.
10 in.

13. Do you see another face that is just like the GREEN face?
Where is it located?

14. Yes, it’s on the bottom.
10 in.
7 in.
10 in.
7 in.

15. 70 in2
Now there are 2 rectangles
that each have an area of 70 sq. in.

16. Now we just need to add all the areas of the sides together.+
70 in2
28 in2
40 in2

17. The total Surface Area for this rectangular prism is=
276 in2

18. It’s your turn to try one!

19. Find the surface area. Area of top and bottom: 3 cm x 2 cm = 6 cm2
Since there are two of these shapes,
6 cm2 x 2 = 12 cm2
6 cm

20. Find the surface area. Area of front and back: 3 cm x 6 cm = 18 cm2
Since there are two of these shapes,
18 cm2 x 2 = 36 cm2
6 cm

21. Find the surface area. Area of both sides: 6 cm x 2 cm = 12 cm2
Since there are two of these shapes,
12 cm2 x 2 = 24 cm2
6 cm

22. Find the surface area. 12 cm2 36 cm2 +24 cm2 72 cm2
Now add up the answers
12 cm2
36 cm2
+24 cm2
72 cm2
6 cm

23. Formula for Surface Area of Rectangular Prisms
length
height
width
SA = 2(lw) + 2(lh) + 2(wh)

24. SA = 6(s2) Formula for Surface Area of a Cube
side
Since all dimensions of a cube are the same, you only need to know the length of one side.
side
side
SA = 6(s2)

25. End of
day 1

26. How much metal is used to make a soup can?
Surface Area of Cylinders
How much metal is used to make a soup can?

27. Surface Area of a cylinder = Area of top + Area of bottom
+ Area of the side
TOP
SIDE
BOTTOM

28. Area of a circle is πr2.
Since there are 2 circles that make up the net of a cylinder then, the area is 2(πr2).

29. C=2πr C h So the area of the rectangle is (2πr)h.
The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the circumference of the circle, since the label wraps once around the can.
C=2πr C h
So the area of the rectangle is (2πr)h.

30. Surface Area of a Cylinder =
Add those two parts together and you have the formula for the surface area of a cylinder.
Surface Area of a Cylinder =
2(π r 2) + (2 π r)h
Circles + Rectangle

31. Example 1:
Find the surface area of this cylinder.
r = 3 cm
h = 6 cm