Question

The cubit is an ancient unit of length based on the distance between the elbow and the tip of the middle finger of the measurer. Assume that the distance ranged from 43 to 53 cm, and suppose that ancient drawings indicate that a cylindrical pillar was to have a length of 9.5 cubits and a diameter of 1.5 cubits. For the stated range, what are the lower value and the upper value, respectively, for the following?
(a) The cylinder's length in meters
lower value:
upper value:

(b) the cylinder's length in millimeters
lower value:
upper value:

(c) the cylinder's volume in cubic meters?
lower value:
upper value:

Answer 1

1 cubit = 43 to 53 cm, L = 9.5 cubits, D = 1.5 cubits.

(a) The cylinder's length in meters
lower value: 0.43 m/cubit * 9.5 cubit = 4.1 m
upper value: 0.53 m/cubit * 9.5 cubit = 5.0 m

(b) the cylinder's length in millimeters
lower value: 4.3*10² mm/cubit * 9.5 cubit = 4.1*10³ mm
upper value: 5.3*10² mm/cubit * 9.5 cubit = 5.0*10³ mm

(c) the cylinder's volume in cubic meters?
lower value: π*(0.43 m/cubit * 1.5/2 cubit)² * (0.43 m/cubit * 9.5 cubit) = 2.7 m³
upper value: π*(0.53 m/cubit * 1.5/2 cubit)² * (0.53 m/cubit * 9.5 cubit) = 5.0 m³