(1) A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 153 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)

radius _________in

length _________in

(2) Find the area of the largest isosceles triangle that can be inscribed in a circle of radius *r* = 6 (see figure).

(3)

Image transcriptions

r A {A l" (a) Solve by writing the area as a function of h. S (b) Solve by writing the area as a function of a. E (c) Identify the type of triangle of maximum area. 0 right 0 obtuse O equilateral

A rectangle is bounded by the x-axis and the semicircle y = v 25 - x2 (see figure). What length and width should the rectangle have so that its area is a maximum? (smaller value) (larger value) 14 12 2 8 10 -2 L

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