Calculating the Rate of Change of Area Covered on a Level Surface

In summary, the problem involves finding the rate of change of the area covered by a circular pattern of liquid on a level surface when the radius is 20cm. This can be solved using derivatives, specifically finding d(SA)/dt.
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Homework Statement



A liquid is being poured onto a level surface making a circular pattern on the surface. Find the rate of change of the area covered on the surface with respect to the radius when the radius is 20cm.

Homework Equations



Surface area = (Pi)r^2

The Attempt at a Solution



Well, what's there to do? If you find the surface area, it's 1256 but what do you do after that? Only one numerical value is given so there's not much to work with. And I don't even know how the answer's supposed to look like - is it going to be in cm, cm^2...Can somebody get me started here...
 
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  • #2
Whenever you see that RATE OF CHANGE is being asked of, then this should indicate that you should be using derivatives.

Now it is asking for rate of change of the Surface area. So find d(SA)/dt.
 
  • #3
The question is asking you how quickly is the area of the puddle increasing, given that the puddle already has a radius of 20cm.
 

1. What is the formula for calculating the rate of change of area covered on a level surface?

The formula for calculating the rate of change of area covered on a level surface is ΔA/Δt, where ΔA represents the change in area and Δt represents the change in time.

2. How do I determine the units for the rate of change of area?

The units for the rate of change of area depend on the units used for area and time. For example, if area is measured in square meters and time is measured in seconds, then the units for the rate of change of area would be square meters per second (m2/s).

3. Can the rate of change of area be negative?

Yes, the rate of change of area can be negative. This indicates that the area is decreasing over time.

4. How is the rate of change of area related to the slope of the graph?

The rate of change of area is equal to the slope of the graph of the area over time. This means that the steeper the slope of the graph, the faster the area is changing.

5. In what situations would calculating the rate of change of area on a level surface be useful?

Calculating the rate of change of area on a level surface can be useful in a variety of situations, such as measuring the growth rate of plants, tracking the expansion of a landmass, or determining the rate at which a liquid evaporates from a surface.

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