Given:
Inner diameter of cylindrical pipe = 4 cm
Water flow rate = 2 L/minute

To find:
Time taken to fill a conical tank

Solution:
Step 1: Calculate the volume of water flowing through the pipe per minute
The inner diameter of the pipe is given as 4 cm. So, the radius of the pipe (r) can be calculated as:
r = diameter/2 = 4/2 = 2 cm

The formula to calculate the volume of a cylinder is:
Volume = π * r^2 * h

Since the water is flowing through the pipe at the rate of 2 L/minute, we can convert it to cm^3/minute by multiplying it with 1000 (1 L = 1000 cm^3):
Water flow rate = 2 * 1000 = 2000 cm^3/minute

Substituting the values in the formula, we get:
Volume of water flowing through the pipe per minute = π * (2)^2 * h = 4πh cm^3/minute

Step 2: Calculate the time taken to fill the conical tank
The conical tank has a radius of 40 cm and a depth of 72 cm.

The formula to calculate the volume of a cone is:
Volume = 1/3 * π * r^2 * h

Substituting the values in the formula, we get:
Volume of the conical tank = 1/3 * π * (40)^2 * 72 = 38400π cm^3

To find the time taken to fill the conical tank, we can divide the volume of the tank by the volume of water flowing through the pipe per minute:
Time taken = Volume of the conical tank / Volume of water flowing through the pipe per minute
= 38400π / (4πh)
= 9600 / h minutes

Step 3: Calculate the value of 'h'
To calculate the value of 'h', we need to find the height of the water level in the conical tank when it is being filled.

The height of the water level in the conical tank can be calculated using the similar triangles property:
h/72 = r/40

Cross-multiplying, we get:
h = (72 * r) / 40
= (72 * 2) / 40
= 3.6 cm

Step 4: Calculate the time taken to fill the conical tank
Now, substituting the value of 'h' in the equation for time taken, we get:
Time taken = 9600 / 3.6
= 2666.67 minutes

Therefore, it would take approximately 2666.67 minutes to fill the conical tank.