Given, length : breadth : height = 3 : 2 : 1
Let the height of block =x m
Then, length of block =3x m
breadth of block =2x m
∴ Volume of the block of stone
=3x×2x×x=6x3 m3
But it is given that volume of the stone = 10368 m3
⟹ x3=103686=1728
⟹ x=3√1728 =(12×12×12)13 =(123)13 =12 m
Hence, the length of the stone = 3 × 12 = 36 m
Breadth of the stone = 2 × 12 = 24 m
Height of the stone = 1 ×12 = 12 m