Question

A tree trunk is 12m in length and has a varying cross-section. The cross-sectional areas at intervals of 3m measured from one end are: 0.52, 0.55, 0.60, 0.63, 0.71, 0.85, 0.97m2 Estimate the volume of the tree trunk.

Answer 1

We will use the Simpson's Rule of volumes to solve this question.

The formula is:

$V=\frac{i}{3}[(A_1+A_7)+4(A_2+A_4+A_6)+2(A_3+A_5)]$

Here, V is the volume, i is the interval and A's are the areas in the table given.

Plugging in the values, we get:

$V=\frac{2}{3}[(0.52+0.97)+4(0.55+0.63+0.84)+2(0.59+0.72)]$

$V=\frac{2}{3}[1.49+8.08+2.62]=8.13$ cubic meters.

Therefore, the estimated volume of the tree trunk is 8.13 cubic meters.