A gutter is to be made from metal sheet where the length of the two of the two sides of the gutter is 4cm and the third side is 5cm. How do you find an angle so that the gutter will carry the maximum amount of water?

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Answer 1 · 2017-07-21T03:18:30

drawn

Let the angle of the gutter be #theta#

Then the volume of the gutter

#V=1/2xx4xx4xxsinthetaxx5 cm^3#

#=>V=40sinthetacm^3#

Volume #V# will be maximum when #sintheta# is maximum i.e #sintheta=1#

This is possible only when #theta=pi/2#