# Peeling the Apple or the Cone That Lost Its Head

##### Age 14 to 16 Challenge Level:

#### First the headless cone :

If this sector had a radius of 10 units what would the area
be?

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?

#### Now for the Apple Peel :

Not a very healthy colour apple this one :

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!) ?

Anyway, what's the amount of peel on an apple whose diameter is
8cm?