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Surface Area

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**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?

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**Surface Area- the sum of the areas of all the faces**

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**What are the dimensions of this rectangle?**

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

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**Do you see another face that is just like the RED face?**

Where is it located?

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Yes, it’s on the back. 10 in. 4 in.

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

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**What are the dimensions of this rectangle?**

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

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**Do you see another face that is just like the BLUE face?**

Where is it located?

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**Yes, it’s on the left side.**

7 in. 4 in. 4 in. 7 in.

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

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**Do you see the GREEN face?**

What are the dimensions of this rectangle? 7 in. 10 in.

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**Do you see another face that is just like the GREEN face?**

Where is it located?

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

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

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**Now we just need to add all the areas of the sides together.**

+ 70 in2 28 in2 40 in2

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**The total Surface Area for this rectangular prism is**

= 276 in2

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**It’s your turn to try one!**

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**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

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**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

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**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

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**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

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**Formula for Surface Area of Rectangular Prisms**

length height width SA = 2(lw) + 2(lh) + 2(wh)

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**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)

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End of day 1

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**How much metal is used to make a soup can?**

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

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**Surface Area of a cylinder = Area of top + Area of bottom **

+ Area of the side TOP SIDE BOTTOM

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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).

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**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.

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**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

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

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