The volume of a cuboid is 1536 m3. Its length is 16 m, and its breadth and height are in the ratio 3 : 2.

Length of the cuboid = 16 m
Suppose that the breadth and height of the cuboid are 3x m and 2x m, respectively.

Then $1536=16 \times 3 x \times 2 x$

$\Rightarrow 1536=16 \times 6 x^{2}$

$\Rightarrow x^{2}=\frac{1536}{96}=16$

$\Rightarrow x=\sqrt{16}=4$

∴ The breadth and height of the cuboid are 12 m and 8 m, respectively.