The cubit is an ancient unit of length based on the distance between the elbow a

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 7.0 cubits and a diameter of 2.5 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:

(No Response) m



upper value:

(No Response) m


(b) the cylinder's length in millimeters



lower value:

(No Response) mm



upper value:

(No Response) mm


(c) the cylinder's volume in cubic meters?



lower value:

(No Response) m3



upper value:

(No Response) m3

Explanation / Answer

In order to find the lower value, we use the lower value of cm for the cubit and do the opposite for the larger value. (a) Lower Value: 7.0 cubits * (43 cm/1 cubit) * (1 m/100 cm) = 3.01 meters Upper Value: 7.0 cubits * (53 cm/1 cubit) * (1 m/100 cm) = 3.71 meters (b) Now we just covert the meters into millimeters by multiplying by 1000 Lower Value: 3.01 meters * 1000 = 3010 millimeters Upper Value: 3.71 meters * 1000 = 3710 millimeters (c) Now we do the same method we used for (a) to find the radii of the two cylinders using the upper and lower values, then use the formula for the volume of a cylinder, pi*(r^2)*h Lower Value: r = 2.5/2 = 1.25 cubits 1.25 cubits * (43 cm/1 cubit) * (1 m/100 cm) = 0.5375 meters V = pi*(r^2)*h = pi*((0.5375)^2)*3.01 = 2.732 m^3 Upper Value: 1.25 cubits * (53 cm/1 cubit) * (1 m/100 cm) = 0.6625 meters V = pi*((0.6625)^2)*3.71 = 5.116 m^3

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