Question

Water in the canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Answer 1

Hint: First we need to find the area of water in the canal. We can see that it is in the cuboid. To find the volume of a canal we need to find the length of the canal for 30 minute. Here they have given for 60 minutes. After finding that we use the condition Volume of water in canal = volume of area irrigated. Using this we can solve this.

Complete step by step solution:

Given,

Canal is in the shape of a cuboid, where breadth is 6 m and height is 1.5 m and speed of canal is 10 km/hr. See the below diagram,

Length of canal in 1 hour = 10 km

Length of canal in 60 = 10 km

Then Length of canal in 30 minutes is given by 

\[ = \dfrac{{30}}{{60}} \times 10\]

\[ = 5km\]

\[ = 5000m\],

That is length of canal in 30 minute is = 5000 m

Now volume of a water in canal,

\[v = {\text{Length}} \times {\text{breadth}} \times {\text{height}}\]

\[v = 5000 \times 6 \times 1.5\]

\[v = 45000{m^3}\].

Now we know that

Volume of water in canal = volume of area irrigated.

Volume of water in canal =Area irrigated \[ \times \] height

\[45000{m^3} = Area \times 8cm\]

\[45000{m^3} = Area \times \dfrac{8}{{100}}m\]

\[Area = \dfrac{100}{{8}} \times 45000{m^2}\]

\[Area = 562500{m^2}\].

Thus the area irrigated is \[562500{m^2}\].

Note: An important step that students tend to miss in such problems is the conversion of units of the given quantities. It is important that all the quantities used in a particular formula are following the same system of units. Here we need to be careful in the S.I. unit of the dimensions. That is height and area; everything needs to be in an S.I unit. Note that 1 cm = 100 m. Also 1 km= 1000 m. using this we have converted the given data in S.I units. If we need the final answer in hectares then we need to divide the obtained answer by 10000.