Question

The radius of a circular disc is given as 24 cm with a maximum error in measurement of 0.02 cm 

(i) Use differentials to estimate the maximum error in the calculated area of the disc, 

(ii) Compute the relative error

Answer 1

r = 24 cm, dr = 0.02 cm

(i) Area = A = πr²; dA/dr = π(2r); 

So, dA = 2πrdr

At r = 24cm and dr = 0.02cm

dA = 2π(24)(0.02) = 0.96 πcm² 

(ii) dA/A