A swimming pool has two identical sides in the shape of a trapezium.
All other sides are rectangular.
The length of the pool is 12m.
The width of the pool is 4m.
The depth of the pool is 2.1m at the deep end and 1.1m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10cm from the top of the pool.
Rafa turns on the hosepipe at09 00 on Monday and water fills at a rate of 200ml per second.
When the pool is full, Rafa turns of the tap. At what time wil this be?
Show your working out.
I visualize two trapezoids as the side walls and rectangles as the end walls.
Volume = area of side wall x width
= 12 ((1.1 + 2.1)/2) ( 4) = 76.8 m^3
= 76.8(1000) L
= 76800 L
200 ml/sec = .2 L/sec
so time taken = 76800/.2 seconds
= 384000 seconds
= 6400 minutes
= 106.6667 hours or 4.44444.. days
= 4 days, 10 hours , 40 minutes
I will let you compute the time he turns off the tap
5:40
To find out when the pool will be full, we first need to calculate the volume of the pool.
Since the pool has two identical trapezium sides, we can calculate the area of one trapezium side and multiply it by 2 to get the total surface area of the sides.
The formula for the area of a trapezium is:
Area = (base1 + base2) * height / 2
In this case, the bases of the trapezium are the widths of the pool, which is 4m. The height is the difference in depth between the shallow and deep ends, which is 2.1m - 1.1m = 1m.
Area = (4 + 4) * 1 / 2
Area = 8m²
So the total surface area of the two trapezium sides is 8m².
The surface area of the rectangular sides can be found by multiplying the length of the pool (12m) by the height of the shallow end (1.1m).
Area = length * height
Area = 12m * 1.1m
Area = 13.2m²
Since there are two identical rectangular sides, the total surface area of the rectangular sides is 2 * 13.2m² = 26.4m².
The total surface area of the pool can be found by adding the surface areas of the trapezium and rectangular sides:
Total surface area = 8m² + 26.4m²
Total surface area = 34.4m²
To find the volume of the pool, we need to multiply the total surface area by the distance between the surface of the water and the top of the pool, which is 10cm or 0.1m:
Volume = Total surface area * Distance
Volume = 34.4m² * 0.1m
Volume = 3.44m³
Now, we can calculate the time it takes to fill the pool. Rafa fills the pool at a rate of 200ml (0.2L) per second:
Time = Volume / Rate
Time = 3.44m³ / 0.2L/s
Time = 3.44m³ / 0.2L/s * 1000mL/L (to convert from L to mL)
Time = 17,200s
Therefore, it will take 17,200 seconds to fill the pool.
To find out at what time the pool will be full, we need to add 17,200 seconds to the starting time of 09:00 on Monday.
If we assume that there are 60 seconds in a minute and 60 minutes in an hour, we can convert the number of seconds to hours and minutes:
17,200 seconds = 17,200s / (60s/min * 60min/hr)
17,200 seconds = 4.78 hours
Adding 4.78 hours to 09:00, we get the time when the pool will be full:
09:00 + 4.78 hours = 13:47
Therefore, the pool will be full at around 13:47 on Monday.