Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted - Maths - Surface Areas and Volumes

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
root ( 3 ) cm Find the edges of the three cubes

Aakash Sharma · Accepted Answer

Dear Student!

Here is the answer to your query.

Let the edges of the three cubes be 3x, 4x and 5x respectively.

Then their volume $= (3 x)^{3}, (4 x)^{3} and (5 x)^{3}$

$= 27 x^{3}, 64 x^{3}, 125 x^{3}$

Given : The length of the diagonal of the single cube = $12 \sqrt{3} cm$

We know that the length of the diagonal of a cube of side $a = a \sqrt{3}$

⇒ edge of the single cube = 12 cm

Now, volume of the single cube = (12 cm)³ = 1728, cm³

Since the three cubes are melted and converted into single cube

⇒ Sum of volumes of three cubes = volume of single cube

$\Rightarrow 27 x^{3} + 64 x^{3} + 125 x^{3} = 1728 \Rightarrow 216 x^{3} = 1728 \Rightarrow x^{3} = \frac{1728}{216} = 8 \Rightarrow x = 2$

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

Cheers!

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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 root ( 3 ) cm. Find the edges of the three cubes .