Circle Geometry?

Question

I am having a hard time with questions like these. When it is just the circle alone I am good to go, but in this case the cone is overlapping part of the circle... Please help me by showing all your work. Thanks so much.
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A mural of a scoop of ice cream inside an ice cream cone is to be painted on the side of a concession stand. The radius of the icecream is 25.0cm and the radius of the top of the cone is 20.0cm

a) calculate the total area for the ice cream scoop circle

b) calculate the central angle determined by the arc of the ice cream inside the cone

c) calculate the area of the sector ACB (A is on end point of the top of the cone, C is the center of the ice cream scoop and B is the other end point of the top of the cone)

d) Calculate the area of the triangle that ACB forms

e) calculate the area of ice cream to be painted.

Answer 1

Surface Area of scoop = 4pir^2 = 2500 cm^2 (This includes that part of the circle hidden inside the cone).

Central angle = 2 arcsin (.8) = 106.26 degrees.

Area of sector ABC = 106.26/360*pi*25^2 = 579 56 cm^2

Area triangle ABC = 20*sqrt(25^2-20^2)=300cm^2

The area of the segment of the circle hidden inside the cone is 579.56-300m = 279.56cm^2.
Thus the amount of ice cream to be painted is 2500 - 279.56 = 2220.44 cm^2