Introduction: Volume is the amount of space that an object occupies. Surface area is the "outside" area of an object. For a block, this is the total of the areas of all its faces. We are going to create a strange pyramid wall and describe its volume and surface area.

Problem:

1. Each square in the diagram represents a cube whose edge is 1 m. What is the volume of the wall?

   

2. What is the surface area of the wall (include the bottom underside of the wall) if each edge is 1 m?
3. You use a crane to lift up the wall and you build a row of 7 blocks (cubes) for the bottom. You set the original wall on this row. What is the surface area of the new wall (include the bottom underside of the wall)?
4. Your friend builds a wall just like yours with 7 blocks on the bottom row, 5 blocks on the second row, 3 blocks on the third row, and 1 block on the top row. Each edge of the blocks she uses is 1.5 m long. What is the volume of her wall? What is the surface area of her wall? Show your work.
5. Two large walls are built using blocks whose edges are each 1 m long. The first wall has 15 rows of blocks (29 blocks on the bottom row, 27 blocks on the second row, 25 blocks on the third row, and so on until there is 1 block on the top row). The second wall is identical to the first wall except that it has a 16th row of 31 blocks below the row with 29 blocks. How much greater is the surface area of the second wall compared to that of the first wall? Show your work.

Materials: linking cubes or wooden cubes, pencil, paper, calculator

Geometry,volume, area, patterns,ratio and proportion, critical and creative thinking, communication

  Activity Type:

Group      Individual 

  Assessment:

Scale:    Levels 1-5   
Self     Peer     Teacher 
Include in your portfolio?
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Toward Your Marks?
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