To solve this problem, we can first find the volume of the hemispherical tank and then calculate how long it takes to empty half of that volume at the given rate.
The volume V of a hemisphere can be calculated using the formula:
V = (2/3) * π * r^3
Where:
V = Volume of the hemisphere
π = Pi (approximately 22/7 in this case)
r = Radius of the hemisphere
In this problem, the tank has a diameter of 3 meters, so the radius (r) is half of that, which is 1.5 meters.
Now, let's calculate the volume of the hemisphere:
V = (2/3) * (22/7) * (1.5^3)
V ≈ 14.13 cubic meters
Now, we want to find out how long it takes to empty half of this volume at a rate of 3 4/7 liters per second.
To find the time (t) it takes to empty half of the volume, we can use the following formula:
t = (Volume to be emptied) / (Rate of emptying)
Half of the volume is V/2, and the rate of emptying is 3 4/7 liters per second, which can be written as (31/7) liters per second.
t = (V/2) / (31/7)
Now, let's calculate t:
t = (14.13/2) / (31/7)
To divide by a fraction, we can multiply by its reciprocal:
t = (14.13/2) * (7/31)
t ≈ 1.5 minutes
So, it will take approximately 1.5 minutes to empty half of the tank.
Now, let's convert 1.5 minutes to seconds:
1.5 minutes * 60 seconds/minute = 90 seconds
So, it will take 90 seconds to empty half of the tank.
Therefore, the correct answer is not one of the options provided. The closest option to 90 seconds is approximately 1.5 minutes, which is option B) 12.8 min, but it's not an exact match.
