+0  
 
0
61
2
avatar

If a central angle of $90$ degrees defines an arc on circle $R$ that has the same length as the arc on circle $W$ defined by a $60$-degree central angle, what is the ratio of the area of circle $R$ to the area of circle $W$? Express your answer as a common fraction.

Guest Jun 27, 2018
 #1
avatar
0

Arc Length = [90 x pi/180 x R] =[60 x pi/180 x W], solve for R/W
R/W = 2/3 - ratio of the area of circle R to circle W

Guest Jun 27, 2018
 #2
avatar+88962 
+1

Let R1  be the radius of the first circle

And let R2 be the measure of the second circle

 

So

 

Arc length  =   radius * theta ( in rads )

 

So....since the arc lenghts are equal....

 

R1 * pi/2   = R2 * pi/3

 

R1 / 2  =  R2 / 3

 

R1  =  (2/3)R2

 

So...the area of  the first circle  is

[ pi * (R1) ^2 ]  =    pi *[  (2/3) R2 ] ^2  =  pi  (4/9) (R2)^2

 

And the area of the second circle  is

pi [ R2]^2  

 

So  the ratio  of the area  of the first cirlce to the second  is

 

[ pi * (4/9) (R2)^2 ]               4

_______________  =       ____

[ pi * (R2)^2 ]                        9

 

 

cool cool cool

CPhill  Jun 27, 2018

33 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.