Question

A beam 4m long, 50cm wide and 20cm deep is made of wood which weighs 25$kg/m^3$. Find the weight of the beam.

Answer 1

Hint:

Volume of a rectangular solid is \[l \times b \times h\]
Where,
$l$ is the length of the rectangular solid,
$b$ is the breadth of the rectangular solid and
$h$ is the height of the rectangular solid.
Beam is a rectangular solid with given length, breadth, height. The volume of the beam can be calculated by the above formula.
Since it is made of the wood which weight is given so we can find the weight of the beam by multiplying the weight of the wood with the volume of the beam.

Complete step by step answer:
It is given that the beam is 4m long, 50cm wide and 20cm deep.
$l = 4m$,
$b = 50cm = 0.5m$ and
$h=20cm = 0.2m$
Since beam is a rectangular solid, so the volume of the beam is \[l \times b \times h\]
On substituting the known values and solving the values we get,
\[ = 4 \times 0.5 \times 0.2\]
Volume of the beam\[ = 0.4{m^3}\]
It is also given that the beam deep is made of wood which weighs $25kg/m^3$
So the weight of $1m^3$ wood = $25kg$
Then the weight of $0.4m^3$ wood $=25\times0.4$
The weight of $0.4m^3$ wood =10 kg

$\therefore$ The weight of the beam is 10kg.

Note:
We have used, \[1{\rm{ }}m = 100cm\]
While finding the weight of the beam we should multiply the weight of the wood given and the volume of the solid here weight of wood for 1 metre cube is given but the volume we have got is less than one so we get the weight of the beam less than the given weight of the wood.