Radius of Circular Disk

Question

The radius of a circular disk is given as 23 cm with a maximal error in measurement of 0.2 cm. Use differentials to estimate the following.

(a) The maximum error in the calculated area of the disk.

(b) The relative maximum error.

(c) The percentage error in that case.

Answer 1

(a)

Area of a disk: A=(pi)*r²=pi(23cm)^2=1661.903 cm^2

Take the derivative of A with respect to r, resulting in your equation for maximum error in area:

dA=2*pi*r*dr

Now plug in your values

dA=2*pi*(23cm)*(0.2cm)=28.903 cm^2

(b)

Relative error = dA/A=28.903/1661.903 = 0.0174

(c)

Percent error = 100*(relative error) % = 100*(0.0174) = 1.739 %