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Cutting a Cube

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

Covering Cups

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Picture of six cups in a triangle

Lyndon joined me to talk about this month's problems and took this picture in my kitchen.

The aim is to make a box that will contain all the cups and have as small a surface area as possible (to keep production costs low).

N.B. I am assuming that the mugs will all be facing up in the box and not stacked, but you could make other assumptions if you like.

What shape and dimensions would your box have?

A cup has a height of 83mm and diameter of 85mm.