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The logo for a new company is a circle divided into 24 equally sized sectors. Six of the sectors are white, and the others are different colors.

The area of one of the white sectors is  13π50 inches squared.

What is the radius of the circle?

 Feb 19, 2020
 #1
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The  angluar  measure  of each of the   sectors =  360/24  =  15°  =  15/180 pi =  pi/12   rads

 

The area,A,  of a sector  with a central  angle measure in rads (theta) is given by

 

A  =(1/2)* r^2  *(theta)

 

13pi/50  = (1/2) *r^2*  ( pi/12)

 

13/50  = r^2 / 24       

 

24*13  / 50    = r^2

 

312/50 =  r^2

 

sqrt  (312/50)   =  r  ≈  2.5 in

 

 

cool cool cool

 Feb 19, 2020
edited by CPhill  Feb 19, 2020
 #2
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13pi/50 ???        Is it not  13π50    or  13* pi * 50

 

Area of a single sector:   As = 13π50 in2    

Radius of a circle             r = sqrt [ ( A* 24 ) / pi ]  = 124.9 inches indecision

Guest Feb 20, 2020
edited by Guest  Feb 20, 2020

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