SOLUTION: The diagram shows a vertical cross -section of a container in the form of invented cone of height 60cm and base radius 20cm. The circular base is held horizontal and uppermost. W

Question 1187852: The diagram shows a vertical cross -section of a container in the form of invented cone of height 60cm and base radius 20cm. The circular base is held horizontal and uppermost. Water is pured into the container at a constant rate of 40cm^3/s.
i)show that, when the depth of water in the container is x cm, the volume in the container is (pie x^3)/27 cm^3
ii) find the rate of increase of x at the instant when x=2.
Found 3 solutions by Edwin McCravy, mccravyedwin, AnlytcPhil:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!

Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

Because of similar right triangles, The formula for the volume of a cone is Substituting and ,
ii) find the rate of increase of x at the instant when x=2.
Divide both sides by 4 Multiply both sides by Answer: The water level is rising at the rate of 90/π or about 28.6 centimeters per second. Edwin

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