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.

\begin{array}{cccccccc}\text{Height} &amp; 0 &amp; 20 &amp; 40 &amp; 60 &amp; 80 &amp; 100 &amp; 120 \\<br /> \text{Circumference} &amp; 31 &amp; 28 &amp; 21 &amp; 17 &amp; 12 &amp; 8 &amp; 2\end{array}

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.