Simpson’s Rule and the Volume of a Sphere

The Problem :

To estimate the volume of timber in a tree-trunk, "Simpson’s rule" is used. The length of the trunk is measured. The cross-sectional areas at the two ends and the middle are estimated.

Simpson’s rule gives the volume of timber as

Length x [ Area Left end + ( 4 x Area Middle ) + Area Right end ] 6

Use this rule to find the volume of

A    a regular cylinder of radius r and length l

B    a cone of radius r and height l

C    a flower-pot with dimensions shown 

D    a sphere of radius r

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Last modified: June 18, 2007