a hemispherical tank full of water is emptied by a pipe at the rate of 25/7 litres/second.How much time will it take to make the tank half empty,if the tank is 3 metres in diameter?

v = 4/3 pi r^3, so the tank can hold

1/2 * 4/3 * pi * (3/2)^3 = 7.07 m^3 of water

So, it will take

7.07 m^3 / (25/7 L/s) to drain

I'll let you do the conversion from m^3 to liters.

16.5minutes

Given, diameter = 3m

So radius = 3/2 m
Rate at which air is pumped is 25/7 liter per second
Volume of tank = 2/3 πr^3 = 99/14m^3
=99000/14 liters

Since 1 liter of air can be pumped in 7/25 sec

Therefore , 99000/14 liter of air can be pumped in 7/25×99000/14 sec

= 1980 sec
= 33 min

To find the time it takes to make the hemispherical tank half empty, we need to calculate the volume of the tank and then divide it by the rate at which water is being emptied.

1. First, we need to calculate the volume of the hemispherical tank. The volume of a hemisphere can be calculated using the formula V = (2/3)πr³, where r is the radius of the hemisphere.

Given that the diameter of the tank is 3 meters, we can find the radius by dividing the diameter by 2:
radius (r) = diameter / 2 = 3m / 2 = 1.5m.

Now, we can substitute the radius into the formula:
V = (2/3)π(1.5m)³
V = (2/3)π(3.375)m³
V ≈ 7.07m³

2. Since the tank needs to be half empty, the amount of water that needs to be emptied is half of the tank's volume: 7.07m³ / 2 = 3.54m³.

3. The rate at which water is being emptied is given as 25/7 liters per second. To convert liters to cubic meters, we need to divide by 1000 since there are 1000 liters in a cubic meter.
Rate = (25/7) liters/s = (25/7) / 1000 m³/s ≈ 0.00357m³/s.

4. Finally, we can calculate the time it takes to empty half of the tank by dividing the volume by the rate:
time = volume / rate = 3.54m³ / 0.00357m³/s ≈ 990.8 seconds.

Therefore, it will take approximately 990.8 seconds to make the tank half empty.