Aptitude | Mensuration 3D | Question 3

A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of all the smaller cubes?
(A) 2:3
(B) 1:5
(C) 2:7
(D) 1:8


Answer: (B)

Explanation: The volume of the original cube = 53 = 125 cm3.
The volume of a smaller cubes = 13 = 1 cm3.
we will be getting total cubes = 125
The surface area of the larger cube = 6*a2 = 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


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