a pool 5 feet deep with a diameter of 40 feet is filled with water in 50 minutes. how long will it take to fill a pool that is 6 feet deep with a diameter of 36 feet?
since the fill rate is volume/time, and is constant, then just solve
(40^2 * 5)/50 = (36^2 * 4)/x
16 hrs.
16hours
To find out how long it will take to fill a pool that is 6 feet deep with a diameter of 36 feet, we can use a proportion based on the depth and volume of the pool.
First, let's calculate the volume of the first pool:
Radius of the first pool = Diameter / 2 = 40 / 2 = 20 feet
Volume of the first pool = π * (Radius)^2 * Depth = 3.14 * (20)^2 * 5 = 6280 cubic feet
Now, let's set up a proportion based on the volume of the two pools:
Volume of the first pool / Time taken to fill the first pool = Volume of the second pool / Time taken to fill the second pool
6280 cubic feet / 50 minutes = (π * (Radius of the second pool)^2 * 6 feet) / Time taken to fill the second pool
To solve for the Time taken to fill the second pool, we need to find the radius of the second pool.
Radius of the second pool = 36 / 2 = 18 feet
Now, we can solve the proportion:
6280 cubic feet / 50 minutes = (3.14 * (18)^2 * 6 feet) / Time taken to fill the second pool
Cross multiplying, we get:
6280 cubic feet * Time taken to fill the second pool = (3.14 * (18)^2 * 6 feet) * 50 minutes
Dividing both sides by (3.14 * (18)^2 * 6 feet), we can solve for Time taken to fill the second pool:
Time taken to fill the second pool = (6280 cubic feet * 50 minutes) / (3.14 * (18)^2 * 6 feet)
Calculating this value, we get:
Time taken to fill the second pool ≈ 254.73 minutes
Therefore, it will take approximately 254.73 minutes to fill a pool that is 6 feet deep with a diameter of 36 feet.