1. Use differentiation to approximate the maximum error in using 5 cm as the radius of a sphere to calculate its volume if the measurement is off by at most 8 mm. Find the approximation of both the relative and percentage error for the volume.
2. Suppose that fluid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, how fast is the area of the circle increasing when the radius is 4 feet?