a solid cube is cut into two cuboid of equal volumes.find the ratio of the total surface area of the given cube and that of one of the cuboids.
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Let the side of cube = x
Then TSA of cube = 6x2
When the cube is cut into two cuboids of equal volumes then
length = x/2
width = x
height=h
TSA of cuboid = 2(lb+bh+hl) = 2(x22+x2+x22)= 2(2x2)=4x2
TSA of cuboid : TSA of cube = 4x2:6x2= 2:3
Then TSA of cube = 6x2
When the cube is cut into two cuboids of equal volumes then
length = x/2
width = x
height=h
TSA of cuboid = 2(lb+bh+hl) = 2(x22+x2+x22)= 2(2x2)=4x2
TSA of cuboid : TSA of cube = 4x2:6x2= 2:3
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