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Published byEric Barnett Modified over 2 years ago

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How much cardboard does it take to make a cereal box? Have you ever wondered?

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

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

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

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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, its on the left side. 4 in. 7 in. 4 in.

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

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Do you see the GREEN face? What are the dimensions of this rectangle? 10 in. 7 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, its on the bottom. 10 in. 7 in. 10 in. 7 in.

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

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Now we just need to add all the areas of the sides together in 2 28 in 2 40 in 2 28 in 2 70 in 2

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The total Surface Area for this rectangular prism is = 276 in 2

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Its your turn to try one!

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

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

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Find the surface area. 6 cm 3 cm 2 cm Area of both sides: 6 cm x 2 cm = 12 cm 2 Since there are two of these shapes, 24 cm 12 cm 2 x 2 = 24 cm 2

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Find the surface area. 6 cm 3 cm 2 cm Now add up the answers 12 cm 2 12 cm 2 36 cm 2 36 cm cm cm 2 72 cm 2

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

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Formula for Surface Area of a Cube SA = 6(s 2 ) side Since all dimensions of a cube are the same, you only need to know the length of one side.

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End of day 1

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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 BOTTOM SIDE

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

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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. h C=2 π r So the area of the rectangle is (2πr)h. C

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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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