### Three Cubes

Can you work out the dimensions of the three cubes?

### Cubic Conundrum

Which of the following cubes can be made from these nets?

### When the Angles of a Triangle Don't Add up to 180 Degrees

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.

# Peeling the Apple or the Cone That Lost Its Head

#### 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?