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 σA = √σ2S + 4σ2C. Is this correct? If so, explain why. If not, compute the uncertainty in A correctly.