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Question

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cubiod to that of the sum of the surface areas of the three cubes.

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Solution

Let edge of each equal cubes = x
Then, surface area of one cube = 6x2
and surface area of three cubes = 3×6x2=18x2
By placing the cubes in a row,
The length of newly formed cubiod (l) = 3x
Breadth (b) = x
and height (h) = x
Surface area of the cubiod so formed
= 2(l×b+b×h+h×l)
= 2(3x×x+x×x+x×3x)
= 2(3x2+x2+3x2)=2×7x2=14x2
Ratio = 14x2:18x2 = 7:9


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