Cone

Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.

Correct result:

r =  2.67 cm
h =  5.33 cm

Solution:

V=13πr2h x/R=2r/H  r=H2Rx=828x h=2(Rx)=2(8x)  V=13π(828x)22(8x)  V=π82682(8x2x3)  V=π82682(28x3x2) V=0 28x3x2=0 x1=0 283x=0  16=3x  x=5.333 cm r=8285.333=2.67 cm 
h=2(85.333)=5.33 cm



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