Idealization Math Example 3

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Example 3

easy
A student uses the formula for the area of a circle, A=Ļ€r2A = \pi r^2, to estimate the area of a manhole cover. State the idealisation made and whether it is reasonable.

Solution

  1. 1
    Idealisation: the manhole cover is assumed to be a perfect circle with a uniform radius.
  2. 2
    In reality it may be slightly oval or have a raised rim, but these deviations are small.
  3. 3
    The formula gives a good approximation ā€” the idealisation is reasonable for estimation.

Answer

Aā‰ˆĻ€r2Ā (valid:Ā deviationsĀ fromĀ perfectĀ circleĀ areĀ negligible)A \approx \pi r^2 \text{ (valid: deviations from perfect circle are negligible)}
An idealisation is reasonable when the ignored imperfections are small relative to the precision required. For an area estimate, assuming perfect circularity is justified.

About Idealization

Replacing a messy real-world object or process with a perfect, simplified version that captures its essence while ignoring complications.

Learn more about Idealization ā†’

More Idealization Examples

Example 1 easy

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Example 2 medium

The formula for compound interest is [formula]. Explain what idealisations are involved and how the

Example 4 medium

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