SOLUTION: Here is the question: A metal cube of volume 1000cm^3 is melted down and cast into a cuboid 50cm long and 10cm broad. What is the percentage increase in the surface areas of the so

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Here is the question: A metal cube of volume 1000cm^3 is melted down and cast into a cuboid 50cm long and 10cm broad. What is the percentage increase in the surface areas of the so      Log On


   

Question 117424: Here is the question: A metal cube of volume 1000cm^3 is melted down and cast into a cuboid 50cm long and 10cm broad. What is the percentage increase in the surface areas of the solids?
Answer by josmiceli(19441) About Me  (Show Source):
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V+=+1000 cm2
V+=+s%5E3 where s is the length of all the sides
V+=+10%2A10%2A10 cm2
s+=+10cm
The surface area is
A%5B1%5D+=+6%2A10%2A10cm2
A%5B1%5D+=+600cm2
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50%2A10%2As+=+1000 Even though the dimensions change, V can't change
s+=+1000%2F500
s+=+2
50%2A10%2A2+=+1000
Two of the faces are 50%2A10cm2
Two of the faces are 50%2A2cm2
Two of the faces are 2%2A10 cm2
A%5B2%5D+=+2%2A50%2A10+%2B+2%2A50%2A2+%2B+2%2A2%2A10
A%5B2%5D+=+1000+%2B+200+%2B+40
A%5B2%5D+=+1240
The increase in area is A%5B2%5D+-+A%5B1%5D+=+1240+-+1000cm2
1240+-+1000+=+240cm2
The percentage increase is 240%2F1000 = 24% answer