(Q4).Three metal cubes with edges 15 cm, 12 cm and 9 cm respectively are melted together and formed into a simple cube. Find the diagonal of this cube.

Edges l1 = 15 cm, l2 = 12 cm, l3 = 9 cm.

Volume of the resulting cube = Sum of the volumes of the three given cubes

L3 = l13 + l23 + l33

L3 = + +

L3 = + +

L3 = = × ×

∴ Edge of the new cube l = cm

Diagonal =√(3l2)=√(×)

=√(×)=√()=cm.