Find the area of sector in a circle in terms of pi. (Geometry)

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Discussion Overview

The discussion revolves around calculating the area of a sector in a circle using the angle in degrees and expressing the result in terms of pi. The focus is on the mathematical reasoning and application of the formula for the area of a sector.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant initially presents the formula for the area of a sector as \( \frac{270}{360} \times \pi r^2 \) but is unsure of the next steps.
  • Another participant simplifies the fraction \( \frac{270^{\circ}}{360^{\circ}} \) to \( \frac{3}{4} \) and provides the area formula as \( A = \frac{3}{4} \pi r^2 \).
  • A third participant suggests that the radius \( r \) is 12m and calculates the area as \( 108\pi \), questioning the correctness of this result.
  • A subsequent reply confirms that \( 108\pi \) is indeed correct.

Areas of Agreement / Disagreement

There is agreement on the calculation of the area of the sector as \( 108\pi \), but the initial steps and assumptions about the radius are discussed without further exploration of alternative methods or interpretations.

Contextual Notes

The discussion does not address any potential limitations or assumptions regarding the radius or the applicability of the formula in different contexts.

Etrujillo
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View attachment 8699

So far i have 270/360× (pi)r^ i don't know what to do next please help.
 

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I would first reduce:

$$\frac{270^{\circ}}{360^{\circ}}=\frac{3}{4}$$

And so we now have the area \(A\):

$$A=\frac{3}{4}\pi r^2$$

Can you identify the radius \(r\) of the circle from the diagram?
 
The radius i believe is 12m so when i plug in your formula i get 108pi as the answer. Am i correct?
 
Yes, 108\pi is correct.
 

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