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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.
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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