Question

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.
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Answer 1

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) = a√3

So, 12√3 = a√3

a = 12 cm

x = 12/6 = 2

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

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Answer 2

Answer:

Edges of the three cube is 6,8,10

Step-by-step explanation:

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