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 value of $\sum_{i = 1}^{10} r (i)$ is equal to

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 value of $\sum_{i = 1}^{10} r (i)$ is equal to

TestHub · Accepted Answer

As above, r ( t ) = − k tan θ ⋅ t + R = R − H k R ​ t ∑ i = 1 10 ​ r ( i ) = 10 R − H R k ​ ∑ i = 1 10 ​ i = 10 R − H 55 R k ​ = 5 R [ 2 − H 11 k ​ ]

Mathematics - Application of Derivative Question with Solution | TestHub

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