Question
Question: The cross – section of a swimming pool is a trapezium as shown in the adjacent diagram. The length o...
The cross – section of a swimming pool is a trapezium as shown in the adjacent diagram. The length of the pool is 200m. Water is pumped into it through a pipe of cross section 1.2m2 at a speed of 0.5 km/hr. Find the time needed to fill the pool completely.
Solution
Calculate the area of the trapezium pool by using the formula: - Area = 21× (sum of parallel lines) × distance between the parallel lines. Now, find the volume of the pool by taking the product of Area and the given length of pool. Now, find the volume of water flowing through the pipe by considering the product of cross – section of pipe and speed of water. Multiply the given speed with 1000 to convert it into m/hr. Finally, apply the formula: - Time = (Volume of pool / Volume of water flowing), to determine the required time.
Complete step-by-step answer:
Here, we have been provided a pool with a given cross – section and length and we have to determine the time in which the pool will be filled with water with a given speed and area of cross – section.
Now, the above pool is in the shape of a trapezium, so we have,
⇒ Area of the pool = 21× (sum of parallel lines) × distance between the parallel sides
⇒ Area of the pool = 21× (0.8+1.2)×2
⇒ Area of the pool = 2m2
We know that volume is the product of the area of cross – section and length or height of the object. Here, the length of pool is 200m, so we have,
⇒ Volume of the pool = Area × length
⇒ Volume of the pool = 2 × 200
⇒ Volume of the pool = 400m3
Now, it is given that the pool is being filled with water with a pipe whose area of cross – section is 1.2m2 and speed of pumping the water is 0.5 km/hr. Converting the speed in m/hr, we get,