Although we live in a 3D world, we aren’t always very good at judging the volumes of things. A few years ago I had the idea of exploring our (mis)judgements of volume by making a collection of differently-shaped objects, all of which had a volume of a pint. I didn’t do anything about it at the time, but when I discovered recently that Pint of Science in Glasgow was holding Creative Reactions, an art exhibition, I decided to take the hint and get to work.

## Cuboids

These cuboids all have a volume of a pint.

## Optimal shapes

These shapes not only have a volume of a pint, but they are all optimal in terms of surface area:

Of all the cuboids with a volume of a pint, a cube has the smallest surface area.

Of all the cylinders with a volume of a pint, a cylinder whose height and diameter are equal has the smallest surface area.

Of all the cones with a volume of a pint, a cone whose height is the square root of 2 times its base diameter has the smallest surface area.

And of **all** solid shapes with a volume of a pint, a sphere has the smallest surface area.

I made the cylinder, sphere and cone on a lathe, and the sphere on a bandsaw.

## A quiet pint

Here we have the lowest (most distal) pint of my arm and hand about to pour a pint of beer into the front pint of my face. All the beer-glass shapes are casts of the interiors of pint glasses. I was slightly disappointed by the beer-glass casts; I was hoping that they might seem strikingly small compared to the actual filled beer glasses, but they don’t.

Casting was a new venture for me. My thanks to Amy Grogan and Alys Owen of the casting workshop at Glasgow School of Art for their help and advice.

My thanks also to Laura McCaughey, Marta Campillo Poveda, and Danielle Leibnitz, who organised the exhibition.

A pint of my face.