Question

Gr12 Calculus limits question. A circular oil spill on the surface of the ocean spreads outward. Find the approximate rate of change in the area of the oil slick with respect to its radius when the radius is 100 m

Answer 1

\[area = \pi r ^{2}\]\[\frac{ d }{dr} \pi r ^{2} = 2 \pi r\]\[2 \pi r = circumference\]
therefore the rate of change in area is equal to the circumference of the circle

http://www-math.mit.edu/~dav/01.11ps1sol.pdf