Final answer:
To fill a round pool with a diameter of 115 cm to a depth of 20 cm using a hose that has a flow rate of 34,000 cm³/min, it would take approximately 6 minutes when rounded to the nearest minute.
Step-by-step explanation:
The subject matter involves calculating the time it takes to fill a pool with water using a hose with a specific flow rate, which squarely falls under the category of Mathematics, specifically volume and rate problems. Given a round pool with a diameter of 115 cm and a desired water depth of 20 cm, and a hose with a flow rate of 34,000 cm³/min, we can determine the time it takes to fill it to the required depth.
First, we calculate the volume of water required to fill the pool to the desired depth. The formula for the volume of a cylinder (V) is V = πr²h, where r is the radius and h is the height (depth in this case).
The radius of the pool is half of the diameter, thus r = 115 cm / 2 = 57.5 cm. The desired depth (h) is 20 cm. So the volume (V) can be calculated as:
V = π * (57.5 cm)² * 20 cm
We round the value of π to 3.14 for our calculations, and the volume V can be simplified to:
V = 3.14 * 3306.25 cm² * 20 cm = 207,134.5 cm³
Next, we use the flow rate of the hose to determine the time it takes to fill the pool. With a rate of 34,000 cm³/min, we can divide the total volume by this rate to find the time in minutes:
Time = 207,134.5 cm³ / 34,000 cm³/min ≈ 6.09 minutes
When rounded to the nearest minute, it would take approximately 6 minutes to fill the pool to a depth of 20 cm with the given hose.