Cubes in a Skeleton Cuboid

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Cubes in a Skeleton Cuboid

• An Investigation

2

• Here is a picture of a skeleton cuboid that has
  been
• made by sticking together a lot of cubes, each of
  edge 1cm.
• You can easily check that the base of the
  skeleton cuboid shown above measures 12cm by 6cm
  and that the height of the cuboid is 10cm.

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• Questions-
• 1) How many 1cm cubes have been used to make
  this skeleton cuboid?
• 2) How many 1cm cubes would be needed to make a
  skeletons with the following outside
  measurements?
• (i) 20cm 15cm 10cm
• (ii) 50cm 30cm 20cm
• 3) What is the total surface
• area of the skeleton
• shown ?

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• 4) What are the total surface areas of the
  other sizes of skeletons given in question 2?
• 5) Can you find a formula for the number of
  cubes required if the skeleton
• measures Lcm by Bcm by Hcm
• 6) Can you find a formula for the total surface
  area in terms of L, B and H? How many cubes in a
  skeleton cuboid?

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• Solution
• Let the dimensions of the skeleton cuboid be Lcm,
  Bcm and Hcm.
• The skeleton can be divided up into a number of
  parts -
• 8 corners
• 4 square rods of length (L 2)
• 4 square rods of length (B 2)
• 4 square rods of length (H 2)
• Let C number of cubes in the model.
• Then C 8 4(L 2) 4(B 2) 4(H 2)
• C 4(L B H) 16 or C 4(L B H 4)
• continued on next slide

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• 1. C 4(12 6 10) 16 4(24) 16 96
• 2. (i) C 4(20 15 10) 16 4(45) 16
  164
• (ii) C 4(50 30 20) 16 4(100) 16
  384
• All the cubes in a skeleton have four exposed
  faces, except for the eight corners which have
  three exposed faces.
• Let A total surface area. A 4C 8
• 3.In the given skeleton, A 4(96) 8 376
• 4. (i) A 4(164) 8 648
• (ii) A 4(384) 8 1528
• 5. No. of cubes C 4(L B H) 16
• Total surface area
• A 4C 8 4(4(L B H) 16))
• A 16(L B H) 72