This is a derivative problem related to rate of change. Here is an example:
The problem I need to solve is the same type of problem, but instead of solving for the area, I am solving for radius. Here is the problem:
The answer is:
I am not sure how to set up the equations to solve for the rate at which the radius increases.
Exa n whose radius increases at a constant rate of 2 ft/s. How fast is the area of the spill mple 2 Assume that oil spilled from a ruptured tanker spreads in a circular pat- ter increasing when the radius of the spill is 60 ft? Solution. Let 1 number of seconds elapsed from the time of the spill r = radius of the spill in feet after t seconds A area of the spill in square feet after t seconds (Figure 3.4.2). We know the rate at which the radius is increasing, and we want to find the rate at which the area is increasing at the instant when r = 60; that is, we want to find dr dA dt =2n/s dt given that -60 Since A is the area of a circle of radius r, om a ruptured tanker Differentiating both sides of (1) with respect to t yields dA dt Oil spill Thus, when r = 60 the area of the spill is increasing at the rate of = 27(60)(2)= 240Ï ft2/s~ 754 ft2/s dt r= 60 With some minor variations, the method used in Example 2 can be used to solve a variety of related rates problems. We can break the method down into five steps.
