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The figure below shows circle O. M Which formula can be used to deter Asec = 360 A 360 B Asec = C Asec 180 180 D Aşec

The figure below shows circle O. M Which formula can be used to deter Asec = 360 A 360 B Asec = C Asec 180 180 D Aşec

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

The figure below shows circle O.

 

Which formula can be used to determine the area of the sector bounded by central angle MON?

 
 
A

Asec=x⋅πr2360

  
 
B

Asec=360x⋅πr2

  
 
C

Asec=πrx180

  
 
D

Asec=180πrx

  
The figure shows circle O with a shaded sector MON. Angle MON is marked as \( x^\circ \), and the radius of the circle is \( r \). The question asks which formula can be used to determine the area of the sector bounded by the central angle \( \angle MON \). Options are given as: A. \( A_{\text{sec}} = \frac{x \cdot \pi r^2}{360} \) B. \( A_{\text{sec}} = \frac{360}{x \cdot \pi r^2} \) C. \( A_{\text{sec}} = \frac{\pi r^2}{180} \) D. \( A_{\text{sec}} = \frac{180}{\pi r^2} \) The correct formula to find the area of the sector is: A. \( A_{\text{sec}} = \frac{x \cdot \pi r^2}{360} \) This formula calculates the area of the sector by taking the fraction of the circle’s area, \( \pi r^2 \), proportional to the central angle \( x \) out of a full circle, which is 360 degrees.
Transcribed Image Text:The figure shows circle O with a shaded sector MON. Angle MON is marked as \( x^\circ \), and the radius of the circle is \( r \). The question asks which formula can be used to determine the area of the sector bounded by the central angle \( \angle MON \). Options are given as: A. \( A_{\text{sec}} = \frac{x \cdot \pi r^2}{360} \) B. \( A_{\text{sec}} = \frac{360}{x \cdot \pi r^2} \) C. \( A_{\text{sec}} = \frac{\pi r^2}{180} \) D. \( A_{\text{sec}} = \frac{180}{\pi r^2} \) The correct formula to find the area of the sector is: A. \( A_{\text{sec}} = \frac{x \cdot \pi r^2}{360} \) This formula calculates the area of the sector by taking the fraction of the circle’s area, \( \pi r^2 \), proportional to the central angle \( x \) out of a full circle, which is 360 degrees.
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