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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