Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2.

Calculate the volume of a cone.

Correct result:

V =  881.1 cm3

Solution:

A=126⋅ π180=126⋅ 3.1416180≐2.1991 rad S=415 cm2  S=πs2⋅ A/(2π)  s=2⋅ S/A=2⋅ 415/2.1991≐19.4274 cm r=A⋅ s/(2π)=2.1991⋅ 19.4274/(2⋅ 3.1416)≐6.7996 cm h=s2−r2=19.42742−6.79962≐18.1986 cm  V=13⋅ π⋅ r2⋅ h=13⋅ 3.1416⋅ 6.79962⋅ 18.1986=881.1 cm3

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