Aptitude - Volume and Surface Area - Discussion

Here it is asked ratio be surface area, so why we have used volume formula here? Please explain.

Nice explanation @Hary.

How to get the Ratio from 50/36? Please tell me.

I can't understand it. Someone, please explain it.

Initially we found out the volume of the larger cube which is the sum of the volumes of all the 3 cubes with which it is formed.
So the volume of cube is =(3^3+4^3+5^3) = 216.
From the above result, we can observe that 216=6*6*6. And the length of each edge of the larger cube is "6". And surface area of each face of a cube is =(6*6).
The surface area of all the 6 faces = 6*(6*6).
Now in the same way the surface area of all the 6 faces of all cubes = 6*(3*3+4*4+5*5).
the ratio is obtained by dividing both the values.
= 6*(3*3+4*4+5*5) / 6*(6*6)
= 9+16+25 / 36
= 50 / 36
= 25:18

Good, Thanks @Tarifa.

While showing it shows 62 instead of 36 watch it (in denominator).

Read the question carefully "total surface areas of the smaller cubes" that means the summation of surface areas for all the smaller three cubes. That's why it is 6* (3*3+4*4+5*5).

Total surface area of cube is 6 a^2.
So that 6* (3*3+4*4+5*5) is written .

I don't know why the surface area of a small cube is more than a large cube?

In question they said that large cube is made by melting 3 small cubes, so the surface area of the large cube must be 3times small cube. But why they didn't do that? Can any one answer this?