Question

The area of a courtyard is $3750{{m}^{2}}$. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs. 6.40 per cubic metre.

Answer 1

First of all convert the given height in cm into height in metre by using the conversion : 1 m = 100 cm. Find the volume of the courtyard that is covered with gravel by multiplying its area with the height up to which gravel is raised. Use the formula : Volume = Area $\times$ height. Finally, take the product of this obtained volume with the cost of gravel per cubic metre to obtain the total cost.

Complete step by step answer:
Here, we have been given that the area of a courtyard is $3750{{m}^{2}}$ and we have to determine the cost of covering it with gravel to a height of 1 cm with the given gravel cost Rs. 6.40 per cubic metre.
Now first let us convert the height in cm into height in metre. We know that, 1 m = 100 cm. Therefore, dividing both sides by 100, we get,
$\begin{aligned} & \Rightarrow \dfrac{1}{100}m=1cm \\\ & \Rightarrow 1cm=0.01m \\\ \end{aligned}$
So, we have to cover the courtyard with gravel to a height of 0.01 m.
Now, we have to find the volume of the courtyard that will be covered with gravel. We know that,
Volume = Area $\times$ height
Substituting the value of area and height in the above relation, we get,
$\Rightarrow$ Volume covered with gravel = $3750\times 0.01{{m}^{3}}=37.5{{m}^{3}}$
It is given that gravel costs Rs. 6.40 cubic metres. So, the total cost of gravel can be determined by taking the product of cost per ${{m}^{3}}$ and volume covered. Therefore, we have,
Total cost of gravel
= cost per ${{m}^{3}}$ $\times$ volume covered
= $6.40\times 37.5=240$

Therefore, the total cost of gravel that will cover the courtyard is Rs. 240.

Note: One may note that the rate of gravel has the unit ‘Rs. per ${{m}^{3}}$’, that means cost per unit volume. You may take idea from this, that we have to find the volume that will be covered with gravel so that when we will find the total cost by multiplication, then the unit of volume must get cancelled. So, do not multiply the given rate with the area only as it will give the wrong answer in terms of unit.