Question

Three cubes with sides in the ratio 3 : 4 : 5 are melted to form a single cube whose diagonal is 123 cm. Find the sides of the cube.​

Answer 1

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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.