### Three Cubes

Can you work out the dimensions of the three cubes?

### 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.

### The Spider and the Fly

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

# Tin Tight

##### Stage: 4 Challenge Level:
What are the most efficient proportions for a tin of paint?

"Efficient" could mean different things from different points of view - maybe start by trying to minimise the amount of material needed to make a tin with that volume.

What is the best diameter and height for a tin that contains $1$ litre of paint?

What about a $5$ litre tin?