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Oct 10th, 2005, 01:55 PM
#2
Re: Related Rates
Short edge of trapezoid = 30cm.
Long edge = 80cm.
Hence each right-angle triangle on the sides has base 25cm, because top = 25+30+25= 80cm.
Height of triangle = 50cm. When water is 30cm deep, this is 3/5 of the height of the trough. Similar triangles mean that the watery width of the triangle is thus 15cm. (Check if you like - the angle at the top is arctan(50/25) which is the same no matter how deep the water is).
So the horizontal width of water is 15+30+15 = 60cm. Hence the surface area of the water is 0.6m x 10m.
Not to finish it off for you... ...you know the surface area and you know what volume comes in in 1min, so you can work out the depth arriving in one min.
Which is how fast it is rising.
zaza
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