a cylindrical cake with radius 12cm and height 10cm has a slice cut out. The shape of the top of the slice is a sector of the circle that forms the top of the cake. Exluding the sliced piece, the angle is 320 degrees.

Question

a) Calculate the area on top of the slice that has been cut out.
b) Calculate the volume of the cake that remains after the slice has been removed.
c) Calculate the surface area of the cake that remains after the slice has been removed.

i particularly need to know how to do c) This is bcause I have already worked out the answers to a) and b)

Answer 1

In terms of surface area, does that refer to the remaining frosted area, or does it include the internal area where the slice was removed? (I assume that you will not include the surface area resting on the plate.)

If the former, subtract the area of top of slice from total top area. Use the portion of the remaining circumference times the height for the area of the sides.

If the latter, add 2 times radius times height to the above area.