Solving for Area: An Oil Slick of Radius 3.0 km

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SUMMARY

The discussion centers on the mathematical relationship between the area of a circular oil slick and its radius, specifically when the radius is 3.0 km. The formula for the area of a circle is established as A = πr², where A represents the area and r represents the radius. The conversation clarifies that the derivative, which is 2πr, pertains to the rate of change of the area with respect to the radius, but the primary focus is on the area formula itself. There is no indication in the problem statement regarding rates of change.

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  • Understanding of basic geometry, specifically the area of a circle.
  • Familiarity with the mathematical constant π (pi).
  • Knowledge of derivatives and their application in calculus.
  • Ability to differentiate between area and rate of change concepts.
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  • Study the derivation of the area formula A = πr² for circles.
  • Learn about the concept of derivatives and their application in real-world scenarios.
  • Explore the relationship between area and volume in different geometric shapes.
  • Investigate applications of calculus in environmental science, particularly in modeling oil spills.
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Students studying geometry and calculus, educators teaching mathematical concepts, and professionals in environmental science dealing with oil spill modeling.

Nitrate
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Homework Statement


1. An oil tanker springs a leak creating a circular oil slick that grows until its radius is 3.0 km.

a.) What is the formula describing the relation between the area of the slick and its radius?


Homework Equations


Area of a circle: (pi)r^2


The Attempt at a Solution


Is the equation for a) y = (pi)r^2,
or is it the derivative: y = 2(pi)r?
 
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Nitrate said:
a.) What is the formula describing the relation between the area of the slick and its radius?
I think you mean the difference between the RATE OF CHANGE of the area of the slick and that of the radius , please make it clear .
 
The formula you give A= \pi r^2 relates the area of a circle to its radius. There is nothing said in your problem, at least the part you posted, about rates of change.
 

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