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johnjan Group Title

a 3x3x3 cube is built out of 27 1x1x1 blocks. Then, seven 1x1x1 blocks are removed. Specifically, the center block from each of the six of the cube is removed and the center block of the cube is removed. What is the total surface area of the modified cube?

  • 5 months ago
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  1. Lena772 Group Title
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    6a^2

    • 5 months ago
  2. sleung Group Title
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    In general, the equation for surface area is \[SA=2lw+2wh+2lh\] Since l,w,h are all the same in a cube they can be renamed as side s, modifying it to \[SA=6s ^{2}\] Since s=1, SA=6 for each 1*1*1 cube. For the original 3*3*3, SA=6*27, or 162. However, the center cube of each face is taken away, so now there are 21 1*1*1 cubes left. Therefore, the total surface area of this modified cube is 6*21, or 126, square units.

    • 5 months ago
  3. johnjan Group Title
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    Thank you. The formula is correct. But there were 7 cubes removed, not 6. so the final answer would be 120.

    • 5 months ago
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