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The following table represents the diameter of the cross section of a wire at continuous heights (feet) above the ground. Assume that each cross section is circular.

Height(ft) 2 6 10 14 18 22 26 30
Diameter 2 2 2.0 1.8 1.6 1.5 1.3 1.2 (feet)

(those should all line up)

a) Approximate how fast the diameter of the tree is changing 22 ft. above the ground. indicate units of measure

b) Use the trapezoid rule to approximate the volume of the tree from 14 ft to 30 ft above the ground. Indicate units of measure

C) the section of the tree from 2 ft to 8 ft is used to make a rectangular beam of length 6 ft. The strength of the beam varies jointly as its width and the square of its height. What should be the width and height of the beam in order to have the strongest beam?

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