Question

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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 $12 \sqrt{3}$. Find the edges of the three cubes.

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Answer 1

Step-by-step explanation:

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Three cubes of 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.

Hard

Solution

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Step -1: Find side of new cube

Let the sides of the metallic cube be3x,4x,5x.

Now according to the problem, these cubes are melted to form a new cube.

Then the volume of the new cube is(3

3

+4

3

+5

3

)x

3

=216x

3

=(6x)

3

.

Then the side of the new cube is 6x.

Step - 2: Find edge of cube

The diagonal of the new cube is 6x

3

cm.

Then according to the problem, 6x

3

= 12

3

or x=2.

So, Edges are 3x=6,4x=8 and 5x=10

Edge of the three cubes is 6 cm, 8 cm, 10 cm respectively.

Hence, the edge of three cubes is 6 cm, 8 cm, 10 cm.

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