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 1 of 3.

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

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?

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.

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.

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).

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).

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?

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?

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.

Anita said:   4 years ago
Here it is asked ratio be surface area, so why we have used volume formula here? Please explain.
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