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The circumference of a tree at different heights above the ground is given in the table below.

Assume that all horizontal cross-sections of the tree are circles.

Estimate the volume of the tree. (Measurements are in inches.)

[tex]\begin{array}{cccccccc}\text{Height} & 0 & 20 & 40 & 60 & 80 & 100 & 120 \\

\text{Circumference} & 31 & 28 & 21 & 17 & 12 & 8 & 2\end{array}[/tex]

I already try to do this by finding the linear function of the radius of the tree from 0-20, 20-40 and so on but this takes a long time. I have to solve this using integrals, is there any faster way to do this?

Assume that all horizontal cross-sections of the tree are circles.

Estimate the volume of the tree. (Measurements are in inches.)

[tex]\begin{array}{cccccccc}\text{Height} & 0 & 20 & 40 & 60 & 80 & 100 & 120 \\

\text{Circumference} & 31 & 28 & 21 & 17 & 12 & 8 & 2\end{array}[/tex]

I already try to do this by finding the linear function of the radius of the tree from 0-20, 20-40 and so on but this takes a long time. I have to solve this using integrals, is there any faster way to do this?

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