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A solid cube is cut into 2 cuboids of equal volumes. find the ratio of the total surface area of the given?

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

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The surface area of a cube is 6*(area of one face) = 6LWThe volume of a cube is LWHacube = 6LWto make two equal cuboids, we cut the cube in half through its height - LW(.5H)The surface area of the cuboid isbase + top + four sidesLW + LW + 4(.5HL)2LW + 2LHacuboid = 2L(W+H)so the ratio of the cube to the cuboid isacube : acuboid6LW : 2L(W+H)now, the important part, since we started with a cube L = W = H, so we can simplify6LL : 2L(L+L)6L^2 : 2L(2L)6L^2 : 4 L^26:43:2

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