Final answer:
To estimate the maximum error in the calculated area of the disk, we can use differentials. The maximum error in the area is approximately 0.24π cm².
Step-by-step explanation:
To estimate the maximum error in the calculated area of the disk, we can use differentials. The formula for the area of a circular disk is A = πr², where r is the radius. Let's define the radius as r = 1.2 cm and the maximum error in measurement as Δr = 0.1 cm. Using differentials, we can calculate the maximum error in the area by taking the derivative of the area formula with respect to the radius:
dA = 2πr dr
Substituting the values r = 1.2 cm and dr = 0.1 cm, we get:
dA = 2π(1.2 cm)(0.1 cm) = 0.24π cm²
Therefore, the maximum error in the calculated area of the disk is approximately 0.24π cm².