Answer:
7.07 cm/min
Explanation:
You want the rate of change of water level in a conical tank 16 m high with radius 4 m when the level is 12 m and the water is draining at 2 m³/min.
Surface area
The level of water in the tank is 12/16 = 3/4 of the height of the tank, so the radius of its surface is (3/4)(4 m) = 3 m. The surface area is ...
A = πr²
A = π(3 m)² = 9π m² ≈ 28.3 m²
Level change
The rate of change of level is the rate of change of volume divided by the surface area:
V'/A = (-2 m³/min)/(9π m²) = -2/(9π) m/min ≈ -0.07074 m/min
The water level is falling at about 7.07 cm/min.