Explanation Given data: y The total edge length of the shape, shown in figure here, is 120 inches and rounded shapes are half circles. Method/Formula used: The function y = f ( x ) is maximum or minimum at point x = c , where f ′ ( c ) = 0 , and it is maximum at x = c when f ″ ( c ) < 0 , and minimum if f ″ ( c ) > 0 . Calculation: The given shape has three parts two half circles AODA and BO’CB and on rectangle ABCD . Let “ r ” be the radius of each half circle, and x the length of the rectangle. Then from figure as total edge length is 120 inch implies π r + x + π r + x = 120 2π r + 2 x = 120 ⇒ π r + x = 60 ................ (1) A B = B C = 2 r ................ (2) Then area of the shape equals area of two half circles + area of the rectangle, i.e. A = 1 2 π r 2 + x × 2 r + 1 2 π r 2 = 2 x r + π r 2 ⇒ A = 2 ( 60 − π r

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is dr…

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Chapter 3.4, Problem 22S

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To find: The dimensions of given shape so that the area enclosed is as large as possible.

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Chapter 3.4, Problem 21S

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Chapter 3 Solutions

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The dimensions of given shape so that the area enclosed is as large as possible.

Solution Summary: The author calculates the dimensions of a given shape so that the area enclosed is as large as possible.

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Chapter 3 Solutions