Maximum of volume

The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?

Correct result:

A =  293.9388 °

Solution:

s=1  V=13 π r2 h  h=s2r2 V=13 π r2 s2r2 V=13 π r2 1r2  V=0 V=dVdr=πr(23 r2)3 1r2 r>0;r1  23 r2=0 r=2/30.8165  o1=2π r=2 3.1416 0.81655.1302 o2=2π s=2 3.1416 16.2832  A=360 o1o2=360 5.13026.2832=120 6=293.9388=2935620"



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