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Suppose that circles A and B have a central angle measuring 100°. Additionally, the length of the intercepted arc for circle A is 35 9 π meters and for circle B is 25 3 π meters. If the radius of circle A is 7 meters, what is the radius of circle B?

A) 9 meters
B) 12 meters
C) 15 meters
D) 18 meters

User Mikia
by
7.8k points

2 Answers

5 votes
15 meters

253π359π = x7
x = 15

When circles have the same central angle measure, the ratio of the lengths of the intercepted arcs is the same as the ratio of the radii.
User Willbill
by
8.2k points
6 votes

Answer:

The correct option is C.

Explanation:

Let the radius of circle B be x.

It is given that circles A and B have a central angle measuring 100°. The length of the intercepted arc for circle A is
(35)/(9)\pi meters and for circle B is
(25)/(3)\pi meters.

The formula of length of arc is


l=r\theta


\theta =(l)/(r)

Since central angel is same for both angles, therefore


(l_1)/(r_1)=(l_2)/(r_2)


((35)/(9)\pi)/(7)=((25)/(3)\pi)/(x)


(35)/(9* 7)\pi={(25)/(3* x)\pi


(5)/(9)\pi=(25)/(3x)\pi


x=(25)/(3)* (9)/(5)=15

The radius of circle B is 15 meters. Therefore the option C is correct.

User Noctis Skytower
by
8.3k points
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