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Question
Three equal cubes are placed adjacently in a row. Find the ratio of the total surfaced area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.
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Solution
Let the side of a cube be 'a' units.
The total surface area of one cube = 6a2
The total surface area of 3 cubes = 3 x 6a2 = 18a2
After joining 3 cubes in a row, length of Cuboid = 3a
Breadth and height of cuboid = a
The total surface area of the cuboid = 2( 3a2 + a2 + 3a2 ) = 14a2
The ratio of total surface area of a cuboid to the total surface area of 3 cubes = `(14a^2) /(18a^2) = 7/9`
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