Suppose a tank leaks toxic chemical. The area affected is a circle centered on the tank. When the spill is first noticed, the circle has a radius of 5000 feet. A response team arrives 30 minutes later, by which time the affected area has grown to a circle with a radius of 5050 feet. How rapidly was the radius of the spill changing between the time the spill was noticed and the arrival of the response team? How rapidly was the area of the spill changing between the time the spill was noticed and the arrival of the response team?
The response team plans to enclose the spill with a circular barrier (see figure). If it will take 90 minutes to set up the circular barrier, how long should it be? Defend your conclusion.
Suppose the response team plans to obtain just enough barrier material to enclose a circular region with a radius of 5200 feet. However, when the material is delivered, they discover that they are 5 feet short; in other words, when they try to enclose a circular area, there is a gap of 5 feet
Since the barrier won't work unless it's closed, they have to use a smaller circle. To make the smaller circle, the members of the response team will take sections of the barrier and walk towards the center. About how far towards the center will they have to walk?
(a) A very small step towards the center.
(b) about a regular walking step towards the center,
(c) several giant steps towards the center.
The barrier will enclose a smaller area. How much less area will be enclosed?
(a) about the area of a smart phone (less than one square foot).
(b) about the area of a sheet of paper (about one square foot).
(c) about the area of a classroom (about two hundred square feet)
(d) about the area of a football field (several thousand square feet).