# 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?

Answer: Option

Explanation:

Volume of the large cube = (3^{3} + 4^{3} + 5^{3}) = 216 cm^{3}.

Let the edge of the large cube be *a*.

So, *a*^{3} = 216 *a* = 6 cm.

Required ratio = | 6 x (3^{2} + 4^{2} + 5^{2}) |
= | 50 | = 25 : 18. | ||

6 x 6^{2} |
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:
3 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 .

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?

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).

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.

= 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?

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