# 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.

Hrushi said:   7 years ago
Nice explanation @Hary.
(1)

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

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

Tuhin said:   7 years ago
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

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

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

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?
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}