the volume of a sphere of diameter d is π/6 d^3
so, you want to empty 1/4 of the sphere (half a hemisphere), or
Ï€/24 * 3^3 = 9Ï€/8 m^3 = 9000Ï€/8 L
At a rate of π L/s, that will take 9000/8 = 1125 seconds
or 18.75 minutes
so, you want to empty 1/4 of the sphere (half a hemisphere), or
Ï€/24 * 3^3 = 9Ï€/8 m^3 = 9000Ï€/8 L
At a rate of π L/s, that will take 9000/8 = 1125 seconds
or 18.75 minutes
First, we need to find the volume of the hemispherical tank. The formula for the volume of a hemisphere is (2/3) * π * r^3, where r is the radius of the base.
Given that the diameter of the base of the tank is 3m, the radius (r) can be calculated by dividing the diameter by 2:
r = 3m / 2 = 1.5m
Now we can calculate the volume of the hemispherical tank:
Volume = (2/3) * π * (1.5m)^3
Volume = (2/3) * 22/7 * 1.5m * 1.5m * 1.5m
Volume = (2/3) * 22/7 * 3.375m^3
Volume = (2/3) * (22/7) * 3.375m^3
Volume ≈ 14.25m^3
Therefore, the volume of half the tank is:
Volume of half the tank = 1/2 * 14.25m^3
Volume of half the tank ≈ 7.125m^3
Next, we need to determine the time it takes to empty this volume at a rate of 22/7 liters per second. To convert the volume from cubic meters to liters, we need to multiply by 1000 (since 1 cubic meter = 1000 liters).
Volume of half the tank in liters = 7.125m^3 * 1000
Volume of half the tank in liters ≈ 7125 liters
Now we can find the time it will take to empty half the tank:
Time = Volume of half the tank / Rate of emptying
Time = 7125 liters / (22/7 liters per second)
Time = 7125 liters / (22/7) liters/second
To divide by a fraction, we multiply by its reciprocal:
Time = 7125 liters * (7/22) seconds/liter
Time = 7125 * 7 / 22 seconds
Time ≈ 2271.59 seconds
Therefore, it will take approximately 2271.59 seconds to empty half the tank.