Question

The cubic is an ancient unit of length based on the distance between that elbow and the tip of the middle finger of the measurer. Assume that the distance ranged from $43$ to $53cm$, and suppose that ancient drawings indicate that a cylindrical pillar was to have a length of $9$ cubits and a diameter of $2$ cubits. For the state range, what are the lower value and the upper value, respectively for
the cylinder's volume in cubic meters?

Answer 1

We can convert length and diameter first and then compute the volume, or first compute the volume and then convert.

We proceed using the latter approach (where $d$ is diameter and $l$ is length).

$V_{cylindermin}=\frac{\pi }{4}l{d}^2=28cubi{t}^3=\left(28cubi{t}^3\right){\left(\frac{0.43m}{1cubit}\right)}^3=2.2m^3$

Similarly, with $0.43m$ replaced by $0.53m$ we obtain $V_{cylinder,max}=4.2m^3$