Show that y=h-2x I cant link the cone and cylinder please help?

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Answer 1 · 2018-02-02T14:53:52

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By the property of similar triangle we can write

#(PQ)/(AO)=(QC)/(OC)#

#=>(PQ)/(AO)=(OC-OQ)/(OC)#

#=>y/h=(h/2-x)/(h/2)#

#=>y/h=1-(2x)/h#

#=>y=h-2x#

Now volume of the cylinder

#V=pixxOQ^2xxPQ=pix^2y=pix^2(h-2x)#

#=>V=pix^2h-2pix^3#

#=>(dV)/(dx)=2pihx-6pix^2#

For maximum value of #V# we have #(dV)/(dx)=0#

So #2pihx-6pix^2=0#

#=>x=h/3#