Water in 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?
Solution:
A figure is drawn below to visualize the canal according to the given question.
From the figure, it can be seen that the shape of the cross-section of the canal is cuboidal. So, the volume of the water, flowing at the speed of 10km/h for 30 minutes will be the same as the volume of water needed to irrigate the area with 8cm of standing water.
To find the volume of water we need to find the length of the water flowing through the canal in 30 minutes at the speed of 10 km/h.
Let us find the volume of the water by using the formula;
Volume of the cuboid = l × b × h, where l, b, and h are the length, breadth, and height of the cuboid respectively.
Volume of the water to needed to irrigate the area = Area to be irrigated × height of the standing water
Volume of water flowing through the canal in 30 minutes = Area to be irrigated × height of the standing water.
Width of the cuboidal canal, b = 6 m
Depth of the cuboidal canal, h = 1.5 m
The speed of water flowing through the canal is 10 km/h
Length of the water flowing through the canal in 1 hour (60 minutes) = 10 km
Length of the water flowing through the canal in 30 minutes = 10 km/2 = 5 km
l = 5 × 1000 m = 5000 m
Height of the standing water, h₁ = 8 cm = 8/100 m = 0.08 m
Volume of water flowing through the canal in 30 minutes = Area to be irrigated × height of the standing water
l × b × h = Area to be irrigated × h1
Area to be irrigated = (l × b × h) / h1
= (5000 m × 6 m × 1.5 m) / 0.08 m
= 562500 m2
Therefore, 562500 m2 area will be irrigated in 30 minutes.
☛ Check: NCERT Solutions Class 10 Maths Chapter 13
Video Solution:
Water in 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?
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.3 Question 8
Summary:
If water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. the area it will irrigate in 30 minutes, if 8 cm of standing water is needed will be 562500 m2.
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