Final answer:
The time it will take to fill the tank completely is approximately 60 years.
Step-by-step explanation:
In order to calculate the time it takes to fill the tank, we need to first find the volume of water that enters the tank each day. Since the funnel is shaped like a cone, we can use the formula for the volume of a cone to find the volume of water collected each day. The formula is V = (1/3)πr^2h, where r is the radius and h is the height.
In this case, the radius of the funnel is 2.2m and the height is unknown. The volume of water collected each day is 32mm, which is equivalent to 0.032m. Plugging these values into the formula, we can solve for h:
V = (1/3)π(2.2)^2h
0.032 = (1/3)π(2.2)^2h
h ≈ 0.013m
Now we can calculate how long it will take to fill the tank by dividing the volume of the tank by the volume of water collected each day. The volume of the tank is length × width × height. In this case, the length is 12m, the width is 6m, and the height is 1.4m:
Volume of tank = 12 × 6 × 1.4 = 100.8m^3
Time to fill tank = Volume of tank / Volume of water collected each day = 100.8 / 0.032 ≈ 3150 days
Therefore, it will take approximately 3150 days to fill the tank completely, which is approximately 60 years.