# 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.
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.

Hary said:
1 decade ago

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

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.

Mukunthan said:
1 decade ago

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 .

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?

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