MATH PROJECT Term Paper Example | Topics and Well Written Essays - 1000 words

MATH PROJECT - Term Paper Example In this work the cross-section of a gutter has been optimized to contain maximum water with a fixed amount (length) of the material of construction. A gutter is to be made of plastic to catch water at the edge of a roof. Naturally the manufactures would like to have a design of a gutter that hold maximum of water with a given amount of material required to fabricate the gutter. Now the problem is what should be the shape of the cross section of the gutter. This appears to be a problem of maxima and minima. Looking at the suggested cross – sections the problem reduces to minimizing the periphery of the gutter cross section for a given area of the cross-section, this is because, while the periphery is made of the construction material (here plastic) the cross-section hold the water. Let us assume that the length of material (here plastic) is ‘l’ and this is folded to make different cross – sections for the gutter with area ‘A’. Now for a given area ‘A’, the length of the material ‘L’ should be minimized or for a given length of the material ‘L’, the cross-sectional area ‘A’ should be maximum. In this analysis, four shapes will be considered – Triangular cross - section, Rectangular Cross –section, Semicircular cross – section and circular cross –