A solid cube is cut into three cuboids of same volumes. what is the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed.
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Let the side of the cube be a.
Total surface area of a cube=6a
2
Length of the each resulting cuboid is half of the side of the cube =
2
a
.
Height and breadth of the cuboid remain same as the side of the cube a.
Total surface area of a cuboid =2(l×b+b×h+l×h)=2(
2
a
×a+a×a+
2
a
×a)=4a
2
Ratio of the total surface area of the given cube and that of one of the cuboids =6a
2
:4a
2
=3:2
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