Water is poured into a conical container at the rate of 10 cm3/sec. the cone points directly down, and it has a height of 20 cm and a base radius of 15 cm. how fast is the water level rising when the water is 2 cm deep (at its deepest point)?

\frac{dh}{dt}_{h=2cm} =\frac{40}{9\pi}\frac{cm}{2}

Explanation:

Hello,

The suitable differential equation for this case is:

As we're looking for the change in height with respect to the time, we need a relationship to achieve such as:

Of course, .

Now, since the volume of a cone is and the ratio or , the volume becomes:

We proceed to its differentiation:

Then, we compute

Finally, at h=2:

Best regards.

c. heat could easily travel through the molecules in the air and escape/enter the flask. removing the air slows down the heat transfer.  

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