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 answer:

A =  293.9388 °

Step-by-step explanation:

s=1  V=31 π r2 h  h=s2r2 V=31 π r2 s2r2 V=31 π r2 1r2  V=0 V=drdV=3 1r2πr(23 r2) r>0;r=1  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 o2o1=360 6.28325.1302=120 6=293.9388=293°5620"



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