If the sector is made into a cone by closing up the gap, what will be the base radius for that cone?
If the cone now suffers a horizontal cut which removes the top and reduces the height of what remains to half the original cone height, what curved surface area does that lower shape now have?
Can you see that an apple can be approximated to a stack of "headless cones" ?
Not very tall ones!
And you could use that curved surface area calculation you did earlier to get an approximation for the total apple peel.
Maybe use a spreadsheet to get improved accuracy with more frustums (the name for headless cones!) ?