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Investigation 1 Building Smart Boxes Rectangular Prisms

Explore how to find surface area and volume of rectangular prisms, with notes, examples, and homework exercises.

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Investigation 1 Building Smart Boxes Rectangular Prisms

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  1. Investigation 1Building Smart BoxesRectangular Prisms Finding surface area and volume of prisms.

  2. Notes for this unit You will have different options for taking notes in this section. The notes will be collected and graded while you are taking the test in this unit • Continue with the current note sheet format • Use the essential questions sheet and take notes in your notebook • Do all notes in your notebook

  3. Homework Book pg 15 A 2,3,5,8, 31 B 2,4,5,10,31, 32 IXL 7th Grade R2 and R16 up to 70 points

  4. Vocab Rectangular Prism a 3D figure with bases as rectangles and lateral faces as parallelograms

  5. Invest 1.1How Big are those Boxes: Finding Volume How do you calculate the surface area and volume of a rectangle prism?

  6. Notes Video Surface Area Amount of area on each side of the prism Find area of each side and add them together Volume Space inside the prism If each square represents 1 cubic unit how many will fill a prism Volume = area of base times height of figure, usually L * W * H

  7. Example Page 9 problem 1.1

  8. Homework You should be able to have the following problems finished Problems 1 and 2

  9. Invest 1.2Optional Containers I: Finding surface area Suppose you design a box in the shape of a rectangular prism with a volume of 24 cm^3. What are the shape and dimension of the box that has minimum surface area?

  10. Notes Determining the best container you can use, without cutting a shape into pieces You could use length and width and height to help with this calculation, if figures are 1 x 1 x 1, how many fit into the shape It may help to have a sketch and just adjust measurements

  11. Example Pg 11 problem 1.2

  12. Homework You should be able to have the following problems finished Problems 3,4 and 31

  13. Invest 1.3Optimal Surface Area II: Finding least Surface Area What are the dimensions of the rectangular prism that has the least surface area for a given volume?

  14. Notes Similar to best area Find the best shape to give you the largest area This would be a regular shape, no matter how you make the sides Square is the best 2D shape Making a cube would help, how to prove this using similar situation as previous problem

  15. Example Pg 12 Problem 1.3

  16. Homework You should be able to have the following problems finished Problem 5

  17. Invest 1.4Compost Containers: Scaling Up Prisms As you change the dimensions of a rectangular prism by a certain scale factor, how do the surface area and volume of the prism change?

  18. Notes Remember how we scaled up a figure with the wumps Need a scale factor Scale factor times original side lengths give you new side lengths We can use scale factor to help find new surface area and volume Use S.F. squared to help find new areas Use S.F. cubed to help find new volumes

  19. Example Pg 13 and 14 problem 1.4

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