Q. 14.7( 12 Votes )

# Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Answer :

We know that,

Volume of cube = a^{3},

where a = side of cube

Now,

Side of first cube, a_{1} = 3 cm

Side of second cube, a_{2} = 4 cm

Side of third cube, a_{3} = 5 cm

Now, Let the side of cube recast from melting these cubes is 'a'.

As the volume remains same,

Volume of recast cube = (volume of 1^{st} + 2^{nd} + 3^{rd} cube)

⇒ a^{3} = a_{1}^{3} + a_{2}^{3} + a_{3}^{3}

⇒ a^{3} = (3)^{3} + (4)^{3} + (5)^{3}

⇒ a^{3} = 27 + 64 + 125 = 216

⇒ a = 6 cm

So, side of cube so formed is 6 cm.

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