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A solid cube is cut into two cuboids exactly at middle asshown in fig 6.31. Find the ratio of the total surface areaof the given cube and that of the cuboid.s. |
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Answer» The surface area of a cub is 6*(area of one face) = 6LWThe volume of a cube is LWHacube = 6LW to 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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