# What is the volume of this tree using integral?

1. Feb 17, 2007

### -EquinoX-

1. The problem statement, all variables and given/known data
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.

$$\begin{array}{cccccccc}\text{Height} & 0 & 20 & 40 & 60 & 80 & 100 & 120 \\ \text{Circumference} & 31 & 28 & 21 & 17 & 12 & 8 & 2\end{array}$$

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

3. 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?

2. Feb 17, 2007