Aptitude | Mensuration 3D | Question 3

Given: A 5 cm cube which is cut into as many smaller cubes of 1 cm as possible. Find what will be the ratio of the surface area of the original cube to that of the sum of the surface areas of all the smaller cubes formed after cuttting? 

(A)

5:4

(B)

5:1

(C)

6:7

(D)

1:5

(E)

None of the above

Answer: (D)

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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