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# cone watch

1. a vessel in the shape of a cone is standing on its apex. water flows in at a steady rate, of 1m^3 per minute. the vessel has a height of 2m and a diameter of 2m when the vessel is 1/8 full find the rate at which the free surface area of the water is increasing. im trying to use the chain rule but dont know what do
2. (Original post by markosheehan)
a vessel in the shape of a cone is standing on its apex. water flows in at a steady rate, of 1m^3 per minute. the vessel has a height of 2m and a diameter of 2m when the vessel is 1/8 full find the rate at which the free surface area of the water is increasing. im trying to use the chain rule but dont know what do
The free-surface area:

The volume of water as a function of time:

Equate the volume of the water at the time when the vessel is one-eighths full with the volume of the water as a function of height of the cone:

, where and are the variable and fixed height of the cone respectively.

Use the relation

Apply the chain rule:

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Updated: January 15, 2017
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