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 = (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.
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:
10 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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