SOLUTION: A cube of white chalk is painted red and cut parallel to a pair of parallel size to form two rectangular solid of equal volume. What percentage of the surface area of each of the n

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Question 152016: A cube of white chalk is painted red and cut parallel to a pair of parallel size to form two rectangular solid of equal volume. What percentage of the surface area of each of the new solid is not painted red.

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Answer: 20% of surface area of each is not painted
Proof:
Before it was cut into half, all the sides are equal right? (a cube is a square with 3-D body). Then it was cut to half and became a rectangular solid. One side of which is not painted.
We have to remember Surface+Area of a rectangular solid:
SA=2LH%2B2LW%2B2WH ---------------------> EQN 1
Important: before it has ALL SIDES EQUAL, and when cut into half there appears now the Length and the Width----> the dimensions of the Width now will be half of the Length: W=%281%2F2%29L, Also the Height remains the same as the Length. Only the Width changed when cut into half.
For the Area of the new rectangular solid, since one side is NOT painted, SA%5Bnew%5D=2LH%2B1LW%2B2WH -------------------> EQN 2
NOW, IF YOU PLUG IN VALUES IN EQN 1 AND EQN 2, REMEMBER L=H, W=%281%2F2%29%0D%0AL and make %28EQN2%2FEQN%29-1%29. Get ABSOLUTE VALUE (no negative)*100% ----------> PERCENTAGE of Surface Area NOT painted.
Hope this helps.
Thank you,
Jojo