Question

A wooden pole is 7m high and 20cm in diameter. Find its weight if the wood weighs 225kg per m3.

Answer 1

Hint: This problem is based on the concept of cylinder. We solve this question with the help of formula i.e. volume of cylinder.
∴Volume of cylinder = $\pi {r^2}h$
Where, r = radius of the cylinder
and h= height of the cylinder
To find its weight, we have to multiply the volume of the cylinder with the given wooden weight of 1m3 i.e. density.
Weight = (Volume)*(Density)

Complete step-by-step answer:
The pole is in the shape of a cylinder so firstly we have to find the volume of the cylinder.
So, the volume of cylinder is given as
$V = \pi {r^2}h$
It is given that
Height of the pole (h) = 7m
Diameter of the pole = 20cm (we have to convert it into meter)
1m = 100cm
$\begin{gathered}
  \therefore {\text{1cm = }}\dfrac{{\text{1}}}{{{\text{100}}}}{\text{m}} \\
  {\text{20cm = }}\dfrac{{20}}{{100}}m = 0.2m \\
\end{gathered} $
Diameter = $\dfrac{{{\text{Radius}}}}{{\text{2}}}{\text{ = }}\dfrac{{{\text{0}}{\text{.2}}}}{{\text{2}}}{\text{ = 0}}{\text{.1m}}$
Radius of the pole (r)= 0.1m
Volume of pole = $\pi {r^2}h$
$\begin{gathered}
  {\text{ = }}\dfrac{{{\text{22}}}}{{\text{7}}}{\text{ \times 0}}{\text{.1 \times 0}}{\text{.1 \times 7}} \\
  {\text{ = 22 \times 0}}{\text{.1 \times 0}}{\text{.1}} \\
  {\text{ = 0}}{\text{.22}}{{\text{m}}^{\text{3}}} \\
\end{gathered} $
∴ Weight for 1m3 = 225kg
Weight of 0.22m3$ = 225 \times 0.22$
$ = 49.5kg$

Hence, weight of the pole = 49.5kg

Note: The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it.
 The weight of the cylinder is based on the radius of the base of the cylinder (r), the height of the cylinder (h), and the density of the material.
Using the volume of a cylinder, the formula for mass (M) from volume (V) and density (mD):
 \[M = V*mD\]
Similarly, we can also find the weight of a hollow cylinder. Firstly we will find the volume and then multiply it by the density of the material to find its weight.