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Question 63

If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to that of the sum of the surface areas of the three cubes will be

Solution

Cube:

Let the sides of the cube be a.

Surface area = 6a^2

Summation of Surface area of 3 cubes = 18a^2

New cuboid:

length (l) = 3a

breadth(b) = a

height(h) = a

Surface area = 2[lb+bh+hl] = 2[3a*a + a*a + a*3a] = 14a^2

Required answer = 14 a^2/18a^2 = 7:9

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