Mr. Daniels bought an above-ground cylindrical swimming pool that has a diameter of 20 feet. He wants to know how long it will take to fill his pool to a depth of 4 feet using his garden hose. It takes him 15 seconds to fill a one-gallon jug. (Note: 1 gallon = 231 cubic inches.)
Time*rate=volume
time=volume/rate=PI*(10)^2 *4 ft^2/rate
now rate is 1gal/15sec*1ft^3/7.48gal * 3600second/hr
rate= 3600/(15*7.48)
so
time=400PI/(3600/(15*7.48))
time=400PI*15*7.48/3600 hr
To calculate the time it will take to fill the pool, we need to find the volume of water required to fill the pool and then divide it by the rate at which Mr. Daniels can fill the pool using his garden hose.
First, let's calculate the volume of the cylindrical swimming pool. The volume of a cylinder can be found using the formula V = πr^2h, where V represents the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the pool (half the diameter), and h is the height or depth of the water in the pool.
Given that the diameter of the pool is 20 feet, we can find the radius (r) by dividing the diameter by 2:
r = diameter / 2 = 20 ft / 2 = 10 ft
Next, we can substitute the values into the volume formula:
V = 3.14159 * 10^2 * 4 ft
Calculating the volume:
V = 3.14159 * 100 * 4 = 1256.636 ft^3
Now we know that the volume of water needed to fill the pool to a depth of 4 feet is approximately 1256.636 ft^3.
Next, we need to calculate how many gallons of water this is. Since 1 gallon is equal to 231 cubic inches, we can convert the volume from cubic feet to gallons using the conversion factor:
1256.636 ft^3 * 7.481 gallons/ft^3 = 9382.133 gallons (rounded to three decimal places)
Hence, approximately 9382.133 gallons of water are needed to fill the pool to a depth of 4 feet.
Now we can calculate the time it will take to fill the pool. We know that it takes Mr. Daniels 15 seconds to fill a one-gallon jug. So we can set up a proportion:
15 seconds / 1 gallon = x seconds / 9382.133 gallons
Cross-multiplying and solving for x, the time in seconds to fill the pool:
15 * 9382.133 = x
x = 140722 seconds (rounded to the nearest second)
Therefore, it will take approximately 140,722 seconds to fill the pool to a depth of 4 feet using Mr. Daniels' garden hose.