If a swimming pool that has a diameter of 40 feet and a height of 5 feet can be filled in 50 minutes, how long will it take to fill a pool that has a diameter of 36 feet and a height of 6 feet?
We will start with calculating the volume of the pool, V
V=πr²h
=π(40/2)²*5
=6283 cubic feet
Filling time = 50 minutes
Filling rate, R, is in cubic feet per minute
R=6283/50=125.66 cubic feet/minute
Volume of second pool
= π(36/2)²*6
= 6107 cubic feet
Filling time
= 6107/R
= 48.6 minutes
87878
To find out how long it will take to fill the second pool, we can use the concept of ratios.
First, let's calculate the volume of the first pool:
The formula to calculate the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Since the diameter of the first pool is 40 feet, the radius is half of the diameter, so the radius is 20 feet.
The height of the first pool is 5 feet.
Using these values, we can calculate the volume of the first pool:
V1 = π(20^2)(5)
V1 = π(400)(5)
V1 = 2000π cubic feet
Now, let's calculate the time it takes to fill the second pool:
The volume of the second pool can be calculated similarly, but with different values.
The diameter of the second pool is 36 feet, so the radius is 18 feet.
The height of the second pool is 6 feet.
Using these values, we can calculate the volume of the second pool:
V2 = π(18^2)(6)
V2 = π(324)(6)
V2 = 1944π cubic feet
Now, we can set up a ratio to determine the time it will take to fill the second pool:
V1 : V2 = Time1 : Time2
Substituting the calculated volumes:
2000π : 1944π = 50 minutes : Time2
Simplifying the ratio by dividing both sides by π:
2000 : 1944 = 50 : Time2
Now, we can solve for Time2:
Cross-multiplying:
2000 * Time2 = 1944 * 50
Dividing both sides by 2000:
Time2 = (1944 * 50) / 2000
Time2 = 48600 / 2000
Time2 = 24.3 minutes
Therefore, it will take approximately 24.3 minutes to fill the second pool.