Final answer:
To half empty a hemispherical tank with a diameter of 3 meters at a rate of 3 4/7 liters per second, it takes approximately 16.5 minutes, which is option A.
Step-by-step explanation:
The question asks how long it will take to half empty a hemispherical tank of water with a diameter of 3 meters at a rate of 3 4/7 liters per second. We'll calculate the volume of the tank, find the volume of half the tank, and then determine the time to empty this volume at the given rate.
First, we calculate the full volume of the hemispherical tank using the formula for the volume of a sphere, V = (2/3)πr3, and then dividing it by two for the hemisphere.
Step 1: Calculate the tank's volume
The radius r of the tank is half its diameter, which is 1.5 meters. Inserting this into the formula and using π = 22/7, we get:
V = (2/3) * (22/7) * (1.5)3 ≈ 14.13 cubic meters.
Since we need to find the time to empty half the tank, we take half of this volume:
Half Volume = 14.13 / 2 ≈ 7.065 cubic meters.
Step 2: Convert the volume to liters
1 cubic meter equals 1000 liters, so:
Half Volume in liters = 7.065 * 1000 ≈ 7065 liters.
Step 3: Divide the half volume by the rate of emptying
The rate is given as 3 4/7 liters per second which is 3 + 4/7 = 25/7 liters per second.
Time = Volume / Rate
Time = 7065 / (25/7)
Time ≈ 1978.2 seconds
Step 4: Convert time to minutes
Time in minutes = 1978.2 seconds / 60 ≈ 32.97 minutes. Since we want the time to half empty the tank, we divide this by 2:
Half Empty Time ≈ 32.97 / 2 ≈ 16.485 minutes, which rounds to 16.5 minutes. Therefore, the correct answer is option A) 16.5 minutes.