A track has the shape of a square capped on two opposite

QUESTION:

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 \(181.2\pm0.1~\mathrm m\).

a. Compute the area of the square and its uncertainty.

b. Compute the area of one of the semicircles and its uncertainty.

c. Let  denote the area of the square as computed in part (a), and let  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  as \(\sigma_A=\sqrt{\sigma_S^2+4\sigma_C^2}\). Is this correct? If so, explain why. If not, compute the uncertainty in  correctly.

Equation Transcription:

Text Transcription:

181.2{+/-}0.1 m

A=S+2C

sigma_A=sqrt{sigma_S^2+4sigma_C^2}