Question

Water in a canal 1.5 m wide and 6 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 desired?

Answer 1

Hint: First find out the volume of water in the reservoir canal in a given time, then equate it to the volume which is to be irrigated, you will get your answer.

Complete step by step solution:

It is given that,

Breadth (b) = 1.5m, Depth or height (h) = 6m, Speed = 10Km/hr

$\Rightarrow$ Length l of canal in 1 hour = 10Km

$\Rightarrow$ Length l of canal in 30 minutes = $\frac{{10}}{2}Km = 5Km$

$\Rightarrow$ Volume of canal is = lbh = $5000 \times 1.5 \times 6\;{m^3}$

Volume of water in canal = Volume of area to be irrigated

$\Rightarrow \;\;\;\;\;\;\;\;\;\;\;5000 \times 1.5 \times 6 = \;{\text{Area irrigated }} \times {\text{ height}}$

Given: height = 8cm = $\dfrac{8}{{100}}m$

$\Rightarrow$ Area irrigated = $\dfrac{{5000 \times 1.5 \times 6}}{{\frac{8}{{100}}}} = \dfrac{{5000 \times 150 \times 6}}{8}$

$\Rightarrow$ Area irrigated = $562500\;{m^2}$

So, this is your desired answer.

NOTE: - Just be careful with the formula you use. A good grasp over mensuration topics will be an added advantage to solve these problems.