Aptitude - Volume and Surface Area - Discussion

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

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?

@Hary.

This shows the area of each side of individual small cubes. For the cube with 3 cm side area of one wall is 3*3 and for 6 wall its 6(3*3).

Likewise for all the 3 smaller cubes. And final is the sum of S.A of all three smaller cubes.

Cube total surface area = 6Xa^2.

So the small cubes total surface area = 6(3^2+4^2+5^2).

Lager Cube former from this cube would be = 6X(12^2).

Because a = 3+4+5.

So, the required ratio small cubes : large cube = 50:144.

If you get it as it is a cube of 6 fine or else take LCM of 216 there you will get as it is a cube of 6.

After that;
a^3=6^3.
Cube roots get cancelled then a=6.
Or
a=3^216
=3^(6)^3
=(6^3)^1/3
=6 (powers get cancelled).

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).

Well the question says "A large cube is formed from the material obtained by melting three smaller CUBES of 3, 4 and 5 cm side. How can be a cubes sides will be different?

Why the total surface areas of smaller cubes are taken as 6* (3*3+4*4+5*5) and why not as sum of individual surface areas of smaller cubes?

216 = 2*108.

= 2*2*54
= 2*2*2*27
= 2*2*2*3*9
= 2*2*2*3*3*3
=2^3 * 3^3 = 6^3.
= 2*3= 6.

i.e 6^3 = 216.

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