# Three metal

Let the edges of cubes be a1, a2 and a3

So, a1 = 3 cm, a2 = 4 cm, and a3 = 5 cm

Explanation: Here the sum of volumes of all three cubes will be equal to the volume of the resulting larger cube as the resulting cube is formed by melting the three cubes.

Volume of cube with edge a1 = v1 = (a1)3

v1 = (3)3

v1 = 27 cm3eqn1

Similarly

Volume of cube with edge a2 = v2 = (a2)3

v2 = (4)3

v2 = 64 cm3eqn2

Volume of cube with edge a3 = v3 = (a3)3

v3 = (5)3

v3 = 125 cm3eqn3

Now let the volume of resulting cube be ‘V’ cm3

So, V = v1 + v2 + v3

V = 27 + 64 + 125 (from eqn1, eqn2 and eqn3)

V = 216 cm3eqn4

Let the edge of resulting cube be ‘a’ cm

So, volume of the resulting cube = V = a3eqn5

Equate equation 4 and 5,

a3 = 216

a = (216)

a = 6 cm

The edge of new cube formed is 6 cm.

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