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in Surface Areas And Volumes by (56.3k points)

Three cubes of a metal whose edges are in the ratio 3: 4: 5 are melted and converted into a single cube whose diagonal is 12√3 cm. Find the edges of the three cubes.

1 Answer

+1 vote
by (30.5k points)
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Best answer

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively.

So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3

= 9x3 + 64x3 + 125x3 = 216x3

Now, let a be the edge of the new cube so formed after melting

Then we have,

a3 = 216x3

a = 6x

We know that,

Diagonal of the cube = (a2 + a2 + a2) = a3

So, 123 = a3

a = 12 cm

x = 12/6 = 2

Thus, the edges of the three cubes are 6 cm, 8 cm and 10 cm respectively.

by (10 points)
edited
3 ka cube 27 hota h 9 nhi
Its a mistake
9+64+125 = 198
And you wrote
9+64+125= 216

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