# 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 1 of 3.

Diya said:   3 years ago
How to get the Ratio from 50/36? Please tell me.
(1)

Sonsm said:   4 years ago
Good, Thanks @Tarifa.

Anita said:   4 years ago
Here it is asked ratio be surface area, so why we have used volume formula here? Please explain.
(1)

Tarifa said:   4 years ago
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).

Mithilesh kumar pandey said:   5 years ago
Total surface area of cube is 6 a^2.
So that 6* (3*3+4*4+5*5) is written .

Swar said:   5 years ago
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?

Roshan said:   6 years ago
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?

Vinod kumar said:   6 years ago
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).

D Priya said:   6 years ago
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.

Ramya said:   7 years ago
How to calculate cube root of 216?