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 5.0 cubits and a diameter of 3.0 cubits. For the stated range, what are the lower values for (a) the cylinder's length in meters, (b) the cylinder's length in millimeters, and (c) the cylinder's volume in cubic meters? What are the upper values for (d) the cylinder's length in meters, (e) the cylinder's length in millimeters, and (f) the cylinder's volume in cubic meters?

Answer 1

a) 215 cm

b) 1290 mm

c) 2.81 m³

d) 265 cm

e) 1590 mm

f) 5.26 m³

Step-by-step explanation:

Lower value

1 cubit = 43 cm

Length of cylinder = 5 cubits

So,

a) Length of cylinder = 5×43 = 215 cm

Diameter of cylinder = 3 cubit

1 cubit = 43 cm = 430 mm

b) Diameter of cylinder = 3×430 = 1290 mm

Radius of cylinder = 129/2 = 64.5 cm

Volume of cylinder

`v=\pi r^2h\\\Rightarrow v=\pi 0.645^2* 2.15\\\Rightarrow v=2.81 m^3`

c) Volume of cylinder = 2.81 m³

Upper value = 53 cm

Length of cylinder = 5 cubits

So,

d) Length of cylinder = 5×53 = 265 cm

Diameter of cylinder = 3 cubit

1 cubit = 53 cm = 530 mm

e) Diameter of cylinder = 3×530 = 1590 mm

Radius of cylinder = 159/2 = 79.5 cm

Volume of cylinder

`v=\pi r^2h\\\Rightarrow v=\pi 0.795^2* 2.65\\\Rightarrow v=5.26 m^3`

f) Volume of cylinder = 5.26 m³