Question

G a tanker has developed a leak in pristine bay and has spilled a considerable amount of oil. the good news is that oil-eating bacteria are eating the oil at the rate of 5 cubic feet per hour. the slick is in the shape of a cylinder, whose height is the thickness of the slick. when the radius of the cylinder is 500 feet, the thickness of the slick is 0.01 ft, and is decreasing at the rate of 0.001 ft/hr.

Answer 1

$V = \pi r^2 h \\ \\ \frac{dV}{dt} = 2\pi r h \frac{dr}{dt} + \pi r^2 \frac{dh}{dt} \\ \\ -5 =2 \pi (500)(.01)\frac{dr}{dt} + \pi (500^2)(-.001) \\ \\ \frac{dr}{dt} = \frac{250 \pi -5}{10 \pi} = \frac{50 \pi - 1}{2 \pi}$