Question 196900: The table below shows how many cubed shaped blocks 4 children have. Each child is asked to make a rectangular prism using all their blocks. Only 1 child can make a rectangular prism that is more than one layer high, wide, and deep. That is, only one child can use alll of his/her blocks to make a prism not having any dimensions that are 1
which child has the appropriate number of blocks to do this, and what would the dimensions be?
why does the choosen number of blocks work and the others do not
draw a digram of the rect. solid that this child could make and determine its surface area.
Amir -10
Barb -21
Carlos -30
Dirk - 35
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! If we look at the problem as a volume problem. Volume of prism is x*y*z dimensions.
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However, to have the defined prism, the total number of blocks, must have 3 integer factors.
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only 30 has 3 factors, 3*2*5 ( 10 = 2*5,,21 =3*7 ,,35 =5*7 )
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to find the SA = 2(3*2) + 2(3*5) +2(2*5) = 12 + 30 + 20 = 62 units squared
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We know the prism is formed of 2 blocks by 3 blocks by 5 blocks high, but we do not know
how big each cube is. The best we can say is the Surface Area is 62 of the side unit squared.
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