Question

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hr. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
(a) $562500{{m}^{2}}$
(b) $562000{{m}^{2}}$
(c) $162500{{m}^{2}}$
(d) None of the above

Answer 1

Hint: To start with, we need to find the check in which shape our given canal is. As there is no specified shape we will consider it to be cuboid shaped. Now, by using the formulas of a cuboid and considering the height needed for our solution is 8 cm, we can get our desired solution.

Complete step by step solution:
According to the question, we are dealing with a canal which is usually in the shape of a cuboid.
We are given, Breadth = 6 m
Height = 1.5 m
And speed of water in the canal = 10 km/hr
So, if we consider a single water particle, it travels 10 km in one hour.
Now, the water particle travels 10 km in 60 minutes.
So, the particle travels a distance of $\left( \dfrac{30}{60}\times 10 \right)$ km in 30 minutes.
Which gives us a result of 5 km = 5000 m.
Thus, the length of the canal is 5000 m.
Now,
Volume of canal = length $\times $ breadth $\times $ height
$\Rightarrow 5000\times 6\times 1.5{{m}^{3}}$
$\Rightarrow 45000{{m}^{3}}$
Again,
Volume of water in canal = Volume of area irrigated
And, Volume of water in canal = Area irrigated multiplied by the value of Height
Thus, we get,
$\Rightarrow 5000\times 6\times 1.5=0.08\times $area irrigated
So, irrigated area = $\dfrac{5000\times 6\times 1.5}{0.08}$ sq m
Simplifying,
Area irrigated = $562500{{m}^{2}}$

So, the correct answer is “Option A”.

Note: In this problem, we are dealing with many units such as cm and m. So, we need to take care of the units to check that all the units are all the same. Otherwise, dissimilarity in units will result into wrong solutions, which is not at all needed.