Question

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

Answer 1

Answer:

The correct option is C.

Step-by-step 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 $\frac{35}{9}\pi$ meters and for circle B is $\frac{25}{3}\pi$ meters.

The formula of length of arc is

$l=r\theta$

$\theta =\frac{l}{r}$

Since central angel is same for both angles, therefore

$\frac{l_1}{r_1}=\frac{l_2}{r_2}$

$\frac{\frac{35}{9}\pi}{7}=\frac{\frac{25}{3}\pi}{x}$

$\frac{35}{9\times 7}\pi={\frac{25}{3\times x}\pi$

$\frac{5}{9}\pi=\frac{25}{3x}\pi$

$x=\frac{25}{3}\times \frac{9}{5}=15$

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

Answer 2

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.