Related rates - tree growth

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Quandaries & Queries

Question from Christy, a student:

How do I go about answering this question, I know I have to find dv/dt, but I'm not sure how to start. Thank you guys so much for helping me previously.

The volume of a certain tree is given by V= 1/12pie C^2h where C is the circumference of the tree at the ground level and h is the height of the tree. If C=5feet and growing at the rate of 0.2feet per yer, and if h=22feet and is growing at 4 feet per year, find the rate of growth of the volume, V.

Hi Christy.

You are starting with the relationship:

So the first step is to take the derivative with respect to time t on each side of the equation:

Now do the derivation, first using the product rule:

The last step is to substitute in the known values.

You are asked to find dV/dt when C is 5 ft, dC/dt is 0.2 ft/yr and dH/dt is 4 ft/yr.

So now you can just substitute these in to find your answer.

Cheers,
Stephen La Rocque and Harley Weston.

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