The following table represents the diameter (feet) of the cross section of a tree at various heights (feet) above the ground. assume that each cross section is circular.
height: 2, 6, 10,14,18, 22, 26, 30 (feet)
diameter: 2.0, 2.0, 2.0, 1.8, 1.6, 1.5, 1.3, 1.2 (feet)
a) approximate how fast the diameter of the tree is changing 22ft. above the ground. indicate units of measure.
b) use the trapezoid rule to approximate the volume of the tree from 14ft to 30ft above the ground. indicate units of measure.
c) the section of the tree from 2 feet to 8 feet is used to make a rectangle beam of length 6 feet. 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?