The measurement of the radius of a circle is found to be 14 inches, with a possible error of 1/4 inch. Use differentials to approximate the possible error and the percentage error in computing the area of a circle.

Answer 1

a = pi r^2
da = 2pi r dr
= 2pi * 14 * 1/4
= 7pi

%err = 7pi/196pi = 1/28

Answer 2

A box is measured to have a length of 15 inches, a width of 8 inches and a depth of 4 inches. From these measurements, we would calculate the volume to be 480 cubic inches. If there is a possible error of up to 0.12 inch in each of the measurements use differentials to estimate the maximum possible error in the calculated volume. (Use V=lbh where V=volume, 1= length(1), 2= width (b), 3= depth (h) )