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Surface Area of Rectangular Prisms and Cubes

Surface Area of Rectangular Prisms and Cubes. Mrs. Bothers East Cobb Middle School (Adapted from Mr. Tauke’s PPT). Surface Area of Rectangular Prisms. Application: How much cardboard does it take to make a cardboard box? The manufacturers have to know this in order to make the boxes.

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Surface Area of Rectangular Prisms and Cubes

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  1. Surface Area of Rectangular Prisms and Cubes Mrs. Bothers East Cobb Middle School (Adapted from Mr. Tauke’s PPT)

  2. Surface Area of Rectangular Prisms Application: How much cardboard does it take to make a cardboard box? The manufacturers have to know this in order to make the boxes.

  3. Another example... When wrapping gifts, you are covering the outside of the box. This is another example of surface area of a rectangular prism.

  4. Good thinking! Looking at the net, you see that TO FIND THE SURFACE AREA OF A RECTANGULAR PRISM, YOU NEED TO FIND THE AREA OF ALL 6 FACES. Let’s explore this idea…

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

  6. Do you see another face that is just like the RED (front) face? Where is it located? Keep an eye on the next screen!

  7. 4 in. 4 in. 10 in. 10 in. Yes, it’s on the back. FRONT BACK

  8. 40 in2 40 in2 Now there are 2 rectangles that each have an area of 40 sq. in.

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

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

  11. 4 in. 4 in. 7 in. 7 in. Yes, it’s on the left side. SIDE 1 SIDE 2

  12. 28 in2 28 in2 Now there are 2 rectangles that each have an area of 28 sq. in.

  13. Do you see the GREEN (top) face? What are the dimensions of this rectangle? 7 in. 10 in.

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

  15. 7 in. 7 in. 10 in. 10 in. Yes, it’s on the bottom. BOTTOM TOP

  16. 70 in2 70 in2 Now there are 2 rectangles that each have an area of 70 sq. in.

  17. 40 in2 40 in2 28 in2 + + 28 in2 + 70 in2 + 70 in2 Now we just need to add all the areas of the sides together.

  18. The total Surface Area for this rectangular prism is 40 + 40 + 28 + 28 + 70+70 = 276 in2

  19. So let's look at the formula... 2(lw) + 2(wh) + 2(lh) 2(40) + 2(28) + 2(70) 80 + 56 + 140 276 in2

  20. Try This One! Use the formula: 2(lw) + 2(wh) + 2(lh) 2(3•4) + 2(4•12) + 2(3•12) 2(12) + 2(48) + 2(36) 24 + 96 + 72 192 cm2

  21. Now consider a cube... It has 6 square faces! Using the example to the left, what is the area of 1 face? 5 • 5 = 25 ft2 Since there are 6 equal faces, what is the surface area? 6 • 25 = 150 ft2 So, for SA of a cube, find the area of one face and then multiply by 6. What do you think the formula is? Yea, good job!! SA Cube = 6s2 (s = length of one side) What is special about a cube?

  22. Find the area of this cube! What is the area of this cube, if its height is 8 in.? 6 • 82 6 • 64 384 in2

  23. Try These: SA Rect. Prism = 2(lw) + 2(wh) + 2(lh) SA Cube = 6s2 1) What is the surface area of a pizza box that has a length of 10 in, a width of 12 in, and a height of 2 in? • How much wrapping paper is needed to cover a box that is 7 cm long, 8 cm wide, and 3 cm tall? • What is the surface area of a Rubik’s Cube that is 3 inches tall? • Which has more surface area, a cube that is 10 in wide, or a rectangular prism that is 12 in wide, 10 in long, and 8 in tall? 1) 328 in2 2) 202 cm2 3) 54 in2 4) cube = 600in2, rect. prism = 592in2

  24. Now, begin your homework. Be sure to use the correct formulas and SHOW ALL YOUR WORK!

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