Question

3 cubes of sides are in the ratio of 3:4:5 are melted to form a new cube of diagonal 15√3.Find the measure of sides of initial cubes

Answer 1

Answer:

Since diagonal of a cube = √3a

15√3=√3a

a=15 cm

Volume of bigger cube =a^3

15^3=3375 cm cube

Now let side of small cube be x

Now sides are 3x,4x,5x

Volume of big cube = vol. of (cube 1+ cube 2+cube 3)

3375=3x^3+4x^3+5x^3

3375=27x^3+64x^3+125x^3

3375=216x^3

x^3=15.625

x=∛ 15.625

x=3.95(approx)

Now 3x=11.85

4x=15.8

5x=19.75

I am not sure but i tried