Question

The edges of three cubes are 3cm, 4cm,5cm. The cubes are melted and recast into a single cube .Find the length of a diagonal of the cube.

Answer 1

volume of first second and third cube equals to=3*3+4*4+5*5
=50cm²

Answer 2

let length of new cube be x cm
volume of the new cube =x^3 cm
total volume (3cubes)=3×3×3+4×4×4+5×5×5
=27+64+125=216
total volume=volume of new cube=x^3=216
x=✓216=6cm
It will form a right angled triangle,
so diagonal=✓6×6+6×6=✓36+36=✓72
✓72=8.48cm(approx.)