A 5 cm cube is cut into as many 1 cm cubes as possible What is the ratio of the surface area of the ...........

Quantitative Aptitude ( CCS) Mensuration 3D

A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?

1 : 6

1 : 5

1 : 25

1 : 125

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Explanation:

The volume of the larger cube = 5³ = 125 cm³.
The volume of each of the smaller cubes = 1³ = 1 cm³. Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a² = 6(5²) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (1²) = 6.
Therefore, surface area of all of the 125, 1 cm³ cubes = 125 * 6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5