# 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 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.

MANVI MEHTA said:   9 years ago
@Hary.

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.