### 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.

# Tin Tight

##### Stage: 4 Challenge Level:

How many cubic centimetres make a litre?

If the tin (cylinder) had a diameter of $10 \; \text{cm}$ what would the height be?

What surface area would this tin have? Don't forget the top and the bottom.

Would a diameter of $20 \; \text{cm}$ have a greater or lesser surface area?

Can you write out a procedure to follow for any diameter you have to try?

Try to follow your procedure and use trial and improvement to get increasingly close to the diameter which gives the lowest value for the complete surface area.

What was the height for that radius value?

What was the proportion between the height and the diameter?

A spreadsheet might be useful once you are sure of your method.