Copyright © University of Cambridge. All rights reserved.

## 'Tubular Stand' printed from http://nrich.maths.org/

A square stand designed to protect surfaces from hot pans is made
from four $10 \; \text{cm}$ long pieces of cylindrical wooden dowel
joined at the corners with $45$ degree mitres.

If the radius of the dowel used to make a stand is $0.5 \;
\text{cm}$, what is the volume of wood used?

If I doubled the volume of wood used but did not change the radius
of the dowel - what would the outside dimension of the stand
be?

If, instead, I doubled the radius of the dowel but kept the same
volume of wood, what would the outside dimension of the stand be
then?

By looking in more detail at the effects of changing one of the
variables at a time, can you describe any relationships between the
volume of wood, the radius and the length of the dowel used?