A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant $= k > 0$ ). Suppose that $r (t)$ is the radius of liquid cone at time t.
The radius of water cone at $t = 1$ is

Question

A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant $= k > 0$ ). Suppose that $r (t)$ is the radius of liquid cone at time t.

The radius of water cone at $t = 1$ is

TestHub · Accepted Answer

As above, d t d r ​ = − k tan θ and r = − ( k tan θ ) t + R r ( 1 ) = − k tan θ + R = − k H R ​ + R = R ( 1 − H k ​ )

Mathematics - Application of Derivative Question with Solution | TestHub

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