Sphere in cone

A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle. Determine the size of the angle with respect to the base of this triangle.

Correct result:

A =  60 °

Solution:

G=1 G:S1=4:3 S1=34 G=34 1=0.75  S1=πr12  r1=S1/π=0.75/3.14160.4886  G=4 πr22  r2=G4π=14 3.14160.2821  tanα=r2:r1 α=arctan(r2/r1)=arctan(0.2821/0.4886)0.5236 rad  α2=2 α=2 0.52361.0472 rad  A=α2=α2 180π=1.0472 180π=60=60



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