Final answer:
To estimate the maximum error in the area of a circular disk, use differentials to find the derivative of the area formula with respect to the radius and multiply it by the maximum error in the radius. The relative maximum error can be found by dividing the maximum error in the area by the actual area. The percentage error can be calculated by multiplying the relative maximum error by 100.
Step-by-step explanation:
To estimate the maximum error in the area of a circular disk, we can use differentials. The area of a circle is given by A = πr^2, where r is the radius. The derivative of A with respect to r is dA/dr = 2πr. We are given that the radius has a maximal error of 0.3 cm, so we can find the maximum error in the area by multiplying the derivative by the maximum error in the radius. Therefore, the maximum error in the calculated area of the disk is approximately 2πr(0.3 cm).
To calculate the relative maximum error, we can divide the maximum error in the area by the actual area. Therefore, the relative maximum error is approximately (2πr(0.3 cm))/(πr^2) = 0.3/r.
To find the percentage error, we can multiply the relative maximum error by 100. Therefore, the percentage error is approximately 100(0.3/r) = 30/r%.