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Question

A solid cube is cut into two cuboids exactly at middle as shown in fig.6.31. Find the ratio of the total surface area of the given cube and that of the cuboid.

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Solution

Let the side of the cube be l cm.
∴ Total surface area of the cube = 6l2 cm2
If the cube is cut from the middle, then the breadth of the cuboid is l2 cm.
Also,
Length of the cuboid = Height of the cuboid = Side of the cube = l cm
∴ Total surface area of the cuboid = 2(lb + bh + hl)
= 2l×l2+l2×l+l×l
= 4l2 cm2

Now,
Total surface area of the cubeTotal surface area of the cuboid=6l2 cm24l2 cm2=32

Hence, the ratio of the total surface area of the given cube to that of the cuboid is 3:2.

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