MATHEMATICS
The principle of integrated fish farming involves farming of fish along with
livestock orland agricultural crops. This type of farming offers great efficiency
in resource utilization, as waste or by product from one system is effectively
recycled. It also enables effective utilization of available farming space for
maximizing production. This system fully utilizes the water body, the water
surface, the land, and the pond silt to increase food production for human
consumption.David, an enthusiastic farmer, interlinks fish and coconut crops.
He made three tanks each of dimension 5.5m x 3m x 3m for growing fish. To
safeguard the fish in the tank, water can be filled only up to 2m. He replaces
water from these tanks once in ten days and stores this water in a cylindrical
overhead tank of length 3.5 m for irrigating 200 coconut trees in his farm. He
follows drip irrigation method so that the trees get equal quantity of water.
*What is the quantity of water required in each Tank in litres to grow the fish?
*While changing water from the fish tanks, the water from all the fish tank exactly fills the cylindrical tank. Then find the diameter of the cylinderical tank.
* The water stored in the cylindrical tank will last for 10 days if all the trees irrigated daily. What is the quantity of water consumed by each tree per day?
*What will be the extra amount of water reached in each fish tank due to a sudden rainfall of 2 cm.
Answers
Answer:
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Given :- He made three tanks each of dimension 5.5m x 3m x 3m for growing fish. To safeguard the fish in the tank, water can be filled only up to 2m. He replaces water from these tanks once in ten days and stores this water in a cylindrical overhead tank of length 3.5 m for irrigating 200 coconut trees in his farm. He follows drip irrigation method so that the trees get equal quantity of water.
(1) What is the quantity of water required in each Tank in litres to grow the fish ?
Solution :-
→ L = 5.5 m
→ B = 3 m
→ H = 2 m { given that , he filled only up to 2m.}
so,
→ Volume of each tank = 5.5 * 3 * 2 = 33 m³ .
now, we know that,
→ 1m³ = 1000 litre
therefore,
→ 33 m³ = 1000 * 33 = 33000 litre (Ans.)
(2) While changing water from the fish tanks, the water from all the fish tank exactly fills the cylindrical tank. Then find the diameter of the cylindrical tank.
Solution :-
given that,
→ Length of cylindrical tank = 3.5 m .
Let radius of cylindrical tank is r m .
so,
→ Volume of three fish tanks = Volume of cylindrical tank.
→ 3 * 33 = (22/7) * r² * 3.5
→ r² = (3 * 33 * 7)/(22 * 3.5)
→ r² = 9
→ r = 3 cm .
therefore,
→ Diameter of the cylindrical tank = Radius * 2 = 3 * 2 = 6 m (Ans.)
(3) The water stored in the cylindrical tank will last for 10 days if all the trees irrigated daily. What is the quantity of water consumed by each tree per day ?
Solution :-
given that,
→ The water stored in the cylindrical tank will last for = 10 days .
and,
→ Total number of coconut trees = 200 .
so,
→ Volume of cylindrical tank = (22/7) * (3)² * 3.5 = 99 m³
then,
→ Volume of cylindrical tank = 1000 * 99 = 99000 litre .
therefore,
→ water irrigated daily = 99000/10 = 9900 litre .
hence,
→ water consumed by each tree per day = 9900/200 = 49.5 litre (Ans.)
(4) What will be the extra amount of water reached in each fish tank due to a sudden rainfall of 2 cm.
Solution :-
→ L = 5.5 m
→ B = 3 m
→ H = 2 m + 2 cm = 2 + 0.02 = 2.02 m { Because of rainfall. }
so,
→ Volume of each tank = 5.5 * 3 * 2.02 = 33.33 m³ .
therefore,
→ The extra amount of water reached in each fish tank = 33.33 - 33 = 0.33 m³ (Ans.)
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