Question

A wooden pole is 7m high and 20cm in diameter. Find its weight if the wood weighs 225kg per ${{m}^{3}}$.

Answer 1

Hint: This type of question is based on the concept of cylinders. We can solve this question with the help of the formula of the volume of the cylinder, that is, $V=\pi {{r}^{2}}h$, where r is the radius and h is the height of the cylinder. And from this question we get, h = 7m. And we will find r by taking half of the diameter given and also we will convert it into m. Then, the weight of the wooden pole if the wood weighs 225kg can be found out by multiplying the volume of the cylinder with the given weight, that is, 225.

Complete step-by-step solution
It is given in the question that a wooden pole is 7m high and 20cm in diameter. And we have been asked to find its weight if the wood weighs 225kg per ${{m}^{3}}$. We know that the pole is in the shape of a cylinder. So, firstly we have to find the volume of the cylinder. So, the volume of a cylinder is given as,
$V=\pi {{r}^{2}}h$
Where r is the radius and h is the height of the cylinder.

And in this question, we have been given the height of the pole, h = 7m, and the diameter of the pole = 20cm. Now, we have to convert cm into m. So, we will use the unitary method to do so.
We know that 1m = 100cm.
So, we can write, $1cm=\dfrac{1}{100}m$.
So, we can write the diameter, that is, 20 cm as $\dfrac{20}{100}m=0.2m$.
We know that radius is half of the diameter, so we get the radius of the pole as,
$r=\dfrac{0.2}{2}=0.1m$
And we know that $\pi =\dfrac{22}{7}$. So, on substituting the values of r = 0.1m, h = 7m and $\pi =\dfrac{22}{7}$ in the formula of volume of a cylinder, we get,
$\begin{align}
  & V=\pi {{r}^{2}}h \\
 & V=\dfrac{22}{7}\times {{\left( 0.1 \right)}^{2}}\times 7 \\
 & V=22\times 0.01 \\
 & V=0.22{{m}^{3}} \\
\end{align}$
Hence, we have got the value of the volume of the pole as $0.22{{m}^{3}}$.
We have been given the question that the weight of the wooden pole for 1 ${{m}^{3}}$ is 225 kg.
So, the weight of wooden pole for $0.22{{m}^{3}}$ is,
$\begin{align}
  & =0.22\times 225 \\
 & =49.5kg \\
\end{align}$
Hence, the weight of the wooden pole is 49.5kg.

Note: While solving this question, the students may make a mistake by not converting all the values into the same unit, as here, they may forget to convert 20 cm to m. Also, as the question is about a wooden pole, some students may not understand how to solve this question, so they must understand that pole is cylindrical in shape and apply the concept of cylinders to solve this question.