Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

The correct answer is: 6

Let the cubes be A, B and C and their sides are x, y and z respectively

x= 3cm

y=4cm

z= 5cm
And let the side if final cube is w
We will first add the volumes of the three cubes A, B and C
Vol(A) + Vol(B) + Vol(C) = x³ + y³ + z³

= 3³ + 4³ + 5³

= 27 + 64 + 125

= 216
The sum of volumes of cubes A , B and C is equal to the resultant cube we obtain by melting these three,
Volume of final cube =  Vol(A) + Vol(B) + Vol(C)

(w)³ = 216
We know that 216 is the cube of 6
Therefore, w = 6
Therefore, the correct option is b) 6 .