# Aptitude - Volume and Surface Area - Discussion

Discussion Forum : Volume and Surface Area - General Questions (Q.No. 14)
14.
A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
2 : 1
3 : 2
25 : 18
27 : 20
Explanation:

Volume of the large cube = (33 + 43 + 53) = 216 cm3.

Let the edge of the large cube be a.

So, a3 = 216         a = 6 cm.

 Required ratio = 6 x (32 + 42 + 52) = 50 = 25 : 18. 6 x 62 36

Discussion:
24 comments Page 3 of 3.

Why we need that 3^2+4^2+5^2?

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

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