Question

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

Answer 1

Length of the cuboid = 16 m
Suppose that the breadth and height of the cuboid are 3x m and 2x m, respectively.
$$\begin{gathered} \mathrm{Then}1536=16\times 3x\times 2x \\ \Rightarrow 1536=16\times 6x^2 \\ \Rightarrow x^2=\frac{1536}{96}=16 \\ \Rightarrow x=\sqrt{16}=4 \end{gathered}$$

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