Question

How many planks of size $2m\times 25cm\times 8cm$ can be prepared from the wooden block 5m long, 70cm broad and 32 cm thick, assuming that there is no wastage?

Answer 1

Hint: First, before proceeding for this, we must know that the plank has the shape of the cuboid and we get the dimensions mentioned in the figure. Then, by using the formula for the volume V of cuboid as the volume of figure never changes when it is reshaped as $V=l\times b\times h$. Similarly, doing the same for the wooden block, we get the volume of two figures. Then, to get the number of planks required to build the wooden block, we need to divide the volume of the wooden block with the volume of the plank.

Complete step by step answer:
In this question, we are supposed to find the value of planks of size $2m\times 25m\times 8m$ can be prepared from the wooden block 5m long, 70cm broad and 32 cm thick, assuming that there is no wastage.
So, before proceeding for this, we must know the that the plank has the shape of the cuboid and we get the dimensions mentioned in the figure as:

Then, by using the formula for the volume V of cuboid as the volume of figure never changes when it is reshaped as:
$V=l\times b\times h$
So, by substituting all the values in the formula, we get:
$\begin{align}
  & V=200\times 25\times 8 \\
 & \Rightarrow V=40000c{{m}^{3}} \\
\end{align}$
Then, we are given in the question that the number of planks requires to form wooden block 5m long, 70cm broad and 32 cm thick which can be drawn as:

Then, by using the formula for the volume V of cuboid as the volume of figure never changes when it is reshaped as:
$V=l\times b\times h$
So, by substituting all the values in the formula, we get:
\[\begin{align}
  & V=500\times 70\times 32 \\
 & \Rightarrow V=1120000c{{m}^{3}} \\
\end{align}\]
Now, to get the number of planks required to build the wooden block, we need to divide the volume of the wooden block with the volume of the plank.
So, by using the above condition, we get the number of planks as:
$\dfrac{1120000}{40000}=28$
So, the number of planks of dimension $2m\times 25cm\times 8cm$ to build a wooden block of dimension 5m long, 70cm broad and 32 cm thick is 28.

Hence, the answer is 28.

Note: Now, to solve these types of questions we need to know some of the basic conversions beforehand so that we can easily proceed in these types of questions. Then, some of the basic conversions are:
$\begin{align}
  & 1m=100cm \\
 & 1cm=\dfrac{1}{100}m \\
\end{align}$