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A Water in a canal, 8 m wide and 6 m deep, is flowing with a speed of 12 km/hour. How much area will it irrigate in one hour, If 0·05 m of standing water is required?
11.52 km² of area will be irrigated in one hour.
Given:
Width of the canal (w) = 8 m
Depth of the canal (d) = 6 m
Speed of water (v) = 12 km/hour
Required height of water for irrigation (h) = 0.05 m
First, let’s calculate the volume of water flowing out in one hour:
Volume of water flown out in 1 hour = Width × Depth × Speed = 8 × 6 × 12,000 m³
Volume of water flown out in 1 hour = 576,000 m³
Since this water will be used to irrigate a certain area, the volume of the irrigated area will be equal to the volume of water flown out in one hour.
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Area × Height = 8 × 6 × 12,000
Given that the height (h) is 0.05 meters:
Area × 0.05 = 8×6×12,000
Area × 0.05 = 576,000
Area = 576,000 / 0.05
Area = 11,520,000 m^2 =11.52 km^2
Area=11,520,000 m^2 = 11.52 km^2
Therefore, 11.52 km² of area will be irrigated in one hour.
Rates and Ratios
Rates and ratios are mathematical concepts used to compare quantities or express relationships between different quantities.
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Rate: A rate compares two different kinds of quantities measured in different units. It is typically expressed as a ratio of two quantities with different units. For example, miles per hour (mph) is a rate that compares distance (miles) to time (hours).
Example: If you travel 60 miles in 2 hours, the rate of your travel is 60 miles / 2 hours = 30 miles per hour.
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Ratio: A ratio compares two quantities of the same kind. It shows how many times one quantity is contained within another. Ratios are often expressed in the form of a fraction, using a colon, or as a decimal.
Example: If a bag contains 5 red marbles and 3 blue marbles, the ratio of red marbles to blue marbles is 5:3 or 5/3.
Rates and ratios are fundamental in various fields, including mathematics, finance, science, and everyday life, for comparison, analysis, and decision-making.
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