**Question:**

An 8 m long cuboidal beam of wood when sliced produces four thousand 1 cm cubes and there is no wastage of wood in this process. If one edge of the beam is 0.5 m, find the third edge.

**Solution:**

Length of the wooden beam $=8 \mathrm{~m}$

Width $=0.5 \mathrm{~m}$

Suppose that the height of the beam is $h \mathrm{~m} .$

Then, its volume $=$ length $\times$ width $\times$ height $=8 \times 0.5 \times \mathrm{h}=4 \times \mathrm{hm}^{3}$

Also, it produces 4000 cubes, each of edge $1 \mathrm{~cm}=1 \times \frac{1}{100} \mathrm{~m}=0.01 \mathrm{~m} \quad(100 \mathrm{~cm}=1 \mathrm{~m})$

Volume of a cube $=(\text { side })^{3}=(0.01)^{3}=0.000001 \mathrm{~m}^{3}$

$\therefore$ Volume of 4000 cubes $=4000 \times 0.000001=0.004 \mathrm{~m}^{3}$

Since there is no wastage of wood in preparing cubes, the volume of the 4000 cubes will be equal to the volume of the cuboidal beam.

i. e., Volume of the cuboidal beam = volume of 4000 cubes

$\Rightarrow 4 \times h=0.004$

$\Rightarrow h=\frac{0.004}{4}=0.001 \mathrm{~m}$

$\therefore$ The third edge of the cuboidal wooden beam is $0.001 \mathrm{~m} .$