A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to
A) 10
B) 50
C) 60
D) 20
Answer
Option (B)
Solution
As per the question from CAT 2017 – Quantitative Aptitude – Geometry – Mensuration,
Ratio of volumes of 5 smaller cubes and original big one = 1 : 1 : 8 : 27 : 27 : 64
Ratio of sides = 1 : 1 : 2 : 3 : 3 : 4
Ratio of areas = 1 : 1 : 4 : 9 : 9 : 16
The sum of the areas of the 5 smaller cubes is 24 parts while that of the big cube is 16 parts. The sum is 50% greater.
Option (B)
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