A track has the shape of a square capped on two opposite sides by semicircles. The length of a side of the square is measured to be 181.2 ± 0.1 m.
a. Compute the area of the square and its uncertainty.
b. Compute the area of one of the semicircles and its uncertainty.
c. Let S denote the area of the square as computed in part (a), and let C denote the area of one of the semicircles as computed in part (b). The area enclosed by the track is A=S+2C. Someone computes the uncertainty in A as 
Is this correct? If so, explain why. If not, compute the uncertainty in A correctly.
(a) Let s be the measured side of the square. Then s = 181.2, ?.=0.1.
The estimated area is S = 
= 32,833.
(b) The estimated area of a semicircle is 
= 12,894.
(c) This is not correct. Let s denote the length of a side of the square. Since S and C are both computed in terms of s, they are not independent. In order to compute 
correctly, we must express A directly in terms of 
.
.
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