A beam 5 m long and 40 cm wide contains 0.6 cubic metre of wood.

Question:

A beam 5 m long and 40 cm wide contains 0.6 cubic metre of wood. How thick is the beam?

Solution:

Length of the beam $=5 \mathrm{~m}$

Breadth $=40 \mathrm{~cm}$

$=40 \times \frac{1}{100} \mathrm{~m} \quad(\because 100 \mathrm{~cm}=1 \mathrm{~m})$

$=0.4 \mathrm{~m}$

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

Also, it is given that the beam contains $0.6$ cubic metre of wood.

i.e., volume of the beam $=0.6 \mathrm{~m}^{3}$

Now, volume of the cuboidal beam $=$ length $\times$ breadth $\times$ height

$\Rightarrow 0.6=5 \times 0.4 \times h$

$\Rightarrow 0.6=2 \times h$

$\Rightarrow h=\frac{0.6}{2}=0.3 \mathrm{~m}$

$\therefore$ The beam is $0.3 \mathrm{~m}$ thick.

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