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Maths Investigation: Drainage Channels.
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Maths Investigation: Drainage Channels. We have been given a length of metal that is 60cm wide. What shape should the metal be bent into so it will hold the greatest volume of water? 60cm X cm X cm Conditions: 1. You must have a symmetrical cross section. 2. The channel must be widest at the top. Semicircle The circumference of the whole circle would be 120cm but the circumference of the semicircle would be 60cm. 120 = 2?R 60 = ?R R = 19.1cm Area = ?R² A = ??x 19.1² A = ? x 3364.76 A = 1145.92 1145.92 is the area of the whole circle so the area of the semicircle is half of that. 1/2A = 573cm² So the area of the semicircle is 573cm² Triangles Example 1 30cm 30cm As there are two sides to a triangle the 60cm length must be split in half, so each side is now 30cm long. But there can also be a variety of angles, ranging from 0º to 90º Here...
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