A spherical tank in a petro-chemical plant has a radius of 5m.

If liquid is entering the tank at a rate of 1500 litres per second and
the depth is 3m how long will it take to fill the tank? Give your
answer in seconds.

rate=volume(time)

rate*time=volume
time=volume/rate= 1.5m^3/(PI*25*3) seconds

To calculate the time it will take to fill the tank, we need to know the volume of the tank and the rate at which liquid is entering.

First, let's calculate the volume of the tank. A spherical tank's volume can be calculated using the formula:

V = (4/3) * π * r^3

where V is the volume and r is the radius. Plugging in the given values:

V = (4/3) * π * (5m)^3
V = (4/3) * π * 125m^3
V ≈ 523.6m^3

Now, let's convert the given flow rate of 1500 liters per second to cubic meters per second. Since 1 liter is equal to 0.001 cubic meters:

Flow Rate = 1500 liters/s * 0.001m^3/liter
Flow Rate = 1.5m^3/s

Finally, we can calculate the time it will take to fill the tank by dividing the volume of the tank by the flow rate:

Time = Volume / Flow Rate
Time = 523.6m^3 / 1.5m^3/s
Time ≈ 349.1 seconds

Therefore, it will take approximately 349.1 seconds to fill the tank.