# 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 2 of 3.
Tuhin said:
7 years ago

I can't understand it. Someone, please explain it.

Hrushi said:
7 years ago

Nice explanation @Hary.

(1)

Nikita said:
7 years ago

How 216 came, can anyone explain me in simple trick?

MAD MATHS said:
7 years ago

Well the question says "A large cube is formed from the material obtained by melting three smaller CUBES of 3, 4 and 5 cm side. How can be a cubes sides will be different?

Raghavi said:
8 years ago

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

Patty said:
8 years ago

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

Ramesh said:
8 years ago

Can anyone explain it in any other ways?

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.

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?

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.

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