Axial cut

The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.

Correct result:

V =  480.6611 cm3

Solution:

S=388.84 cm2 s=2r S=πr2+πrs=πr(r+s) S=πr(r+2r)=3 πr2  r=S/(3π)=388.84/(3⋅ 3.1416)≐6.4232 cm s=2⋅ r=2⋅ 6.4232≐12.8464 cm  h2=s2−r2 h=r⋅ 3=6.4232⋅ 3≐11.1253 cm  V=π⋅ r2⋅ h/3=3.1416⋅ 6.42322⋅ 11.1253/3=480.6611 cm3

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