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Pyramids Question

  1. Sep 2, 2005 #1
    The base of the pyramid is 100 blocks by 100 blocks; each successive layer is one less block wide and deep, until the top layer which is simply one block. Each block is 97 cm wide by 97 cm deep by 63 cm tall.

    If one liter of paint can coat exactly three square meters, how many liters are required to coat the entire exposed surface of the pyramid? Round up to the nearest liter.

    I know what to do but is there a "pattern" that can be used here?

    Paint Used For Side of Blocks:
    = 5050 x width of 97 x height of 63 x 4 sides of a pyramid
    = 123,442,200 cm2 / 10 000
    = 12,344.22 m2 / 3
    = 4114.74 litres of paint

    Paint Used For Top of Blocks:
    = (100 x 100) (97 x 97)
    = 94090000 cm2 / 10 000
    = 9409 m2 / 3
    = 3136.33

    4114.74 + 3136.33
    = 7251.07
    = 7251 L.

    Can I have confirmation that this is right? :smile: =)
    Last edited: Sep 2, 2005
  2. jcsd
  3. Sep 2, 2005 #2
    What is the sum of squares of first 100 numbers? This gives you total periphery. Multiply it with the width and height. You get total exposed surface area. Convert it into sq.mtr.
  4. Sep 2, 2005 #3


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    To cover the top of all blocks.
    So what will you see if you are on the plane, which is above the top of the pyramid, and look straight down the pyramid?
    You will see a 100 blocks x 100 blocks rectangle, right?
    So what is the area of that rectangle? Is it also the area of the top of all blocks you must paint?
    Viet Dao,
    Last edited: Sep 2, 2005
  5. Sep 2, 2005 #4
    yes you have to paint the sides of the blcok and the top of the block
  6. Sep 2, 2005 #5


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    It seems that you got the side of the block correctly, but you got the top of the block incorretly...
    First, why are you multiply by 4 (sides of the pyramid)?
    And if you calculate like that, you will paint all top of the blocks, not just the ones that are exposed.
    Viet Dao,
  7. Sep 2, 2005 #6
    Thank you for that comment. I will correct it.
  8. Sep 2, 2005 #7


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    Yup. Correct.
    But you don't need the 1 + 2 + 3 + ... + 100. :smile:
    See the bolded part of the quote.
    Viet Dao,
  9. Sep 2, 2005 #8
    I am sorry for misguiding.
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