The height of a cone is increasing at a rate of 10 cm/sec and its radius is decreasing so that its volume remains constant. how fast is the radius changing when the radius is 4 cm and the height is 10 cm?

dr/dt = -2 cm/s.

Explanation:

The volume of a cone is given by:

(1)

Let's take the derivative with respect to time in each side of (1).

(2)

We know that:

We can calculate how fast is the radius changing using the above information.

Therefore dr/dt will be:

The minus signs means that r is decreasing.

I hope it helps you!

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