Question 821108: [ A solid wood cube 1 ft on an edge, was sawed into eight smaller congruent cubes. The smaller cubes were then reassembled to form the longest possible rectangular prism. What is the percent change in surface area? (If you can, Please show a step by step solution) ]
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 1 ft * 12 in/ft = 12 in
v = 12^3 = 12*12*12
v/8 = 12*12*12/8
cubedroot(v/8) = cubedroot( 12*12*12/8 )
cubedroot(v/8) = 6 in
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the 8 small cubes are 6 inches per side
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stack the 8 small cubes end-to-end, forming a new rect prism 48 x 6 x 6 inches
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original area = 12*12*6 = 864 sq.in
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prism area = 48*6*4 + 6*6*2 = 1152 + 72 = 1224 sq.in
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% change in area:
1224/864 * 100 = 141.666%
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