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Question
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is
Options
7 : 9
49 : 81
9 : 7
27 : 23
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Solution
Let, a → Side of each cube
So, the dimensions of the resulting cuboid are,
Length(l) = 3a
Breadth (b) = a
Height (h) = a
Total surface area of the cuboid,
=2(lb + bh + hl)
=2[(3a) a + a × a + a (3a)]
= 14 a2
Sum of the surface areas of the three cubes,
= 3 (6a2)
= 18 a2 Required ratio,
=`(14a^2)/(18a^2)`
=7:9
Thus, the required ratio is 7: 9 .
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