Question

A high tech company operates a satellite which can measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 615 ± 1.78 (in meters) and it's width to be 170 ± 1.27 (in meters). They plan to report the area of the field as A±ΔA in units of acres. (1 acre = 4840 square yards & 1 meter = 1.094 yards) What is ΔA?

Answer 1

From the data L=615m

L=1.78m

B=170m

B=1.27m

Let us find the maximum and the minimum area of fileds,

A_max=(L+ L)(B+ B)

=(615+1.78)(170+1.27)

=105635.911m²

A_min=(L- L)(B- B)

=(615-1.75)(170-1.27)

=(613.25)(168.73)

=103473.673m²

The average area is

A=(A_max+A_min)/2

A=(105635.911+103473.673)*0.5

A=104554.792m²

A=104554.792m²((1.094 yards)²/(1 m²)/(1 acres)/(4840 square Yards))

A=23.6328 acres

The uncertanity in the area is ,

A=A_max-A

=105635.911m²-104554.792m²

=1081.119m²

=1081.119m²((1.094 yards)²/(1 m²)/(1 acres)/(4840 square Yards))

=0.24436acres

The total area is

A+ A=(23.6328 0.24436) acres