What is the volume of this tree using integral?

[-EquinoX-]

Homework Statement

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.

[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]

Homework Equations

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

The Attempt at a Solution

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?

 

[Gib Z]

You already posted exactly the same thing here:

https://www.physicsforums.com/showthread.php?t=156720

I posted there, but the only thing I have to add from that is use Simpsons rule in 3 segments to approximate it.