# 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.
Imran said:
1 decade ago

How required ratio come?

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

Mukunthan said:
1 decade ago

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

Arya said:
1 decade ago

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

Harsha said:
9 years ago

@Hary.

This shows the area of each side of individual small cubes. For the cube with 3 cm side area of one wall is 3*3 and for 6 wall its 6(3*3).

Likewise for all the 3 smaller cubes. And final is the sum of S.A of all three smaller cubes.

This shows the area of each side of individual small cubes. For the cube with 3 cm side area of one wall is 3*3 and for 6 wall its 6(3*3).

Likewise for all the 3 smaller cubes. And final is the sum of S.A of all three smaller cubes.

MANVI MEHTA said:
9 years ago

@Hary.

Can you please explain the required ratio step more clearly?

Can you please explain the required ratio step more clearly?

Prasanna said:
9 years ago

Cube total surface area = 6Xa^2.

So the small cubes total surface area = 6(3^2+4^2+5^2).

Lager Cube former from this cube would be = 6X(12^2).

Because a = 3+4+5.

So, the required ratio small cubes : large cube = 50:144.

So the small cubes total surface area = 6(3^2+4^2+5^2).

Lager Cube former from this cube would be = 6X(12^2).

Because a = 3+4+5.

So, the required ratio small cubes : large cube = 50:144.

Ramesh said:
8 years ago

Can anyone explain it in any other ways?

Patty said:
8 years ago

Really I don't know, how to calculate the answer. Please anyone help me.

Raghavi said:
8 years ago

I too can't understand this problem. Someone explains me.

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