Question

Both circle A and circle B have a central angle measuring 50°. The area of circle A's sector is 36π cm2, and the area of circle B's sector is 64π cm2. Which is the ratio of the radius of circle A to the radius of circle B?
A) 3/4
B) 3/7
C) 4/3
D) 5/7

Answer 1

Answer:

A) 3/4

Step-by-step explanation:

Given: Both circle A and circle B have a central angle measuring 50°.

           The area of circle A's sector is 36π cm2.

            The area of circle B's sector is 64π cm2.

We know, area of the circle= $\pi r^{2}$

lets assume the radius of circle A be "$r_1$" and radius of circle B be "$r_2$"

As given, Area of circle A and B´s sector is 36π and 64π repectively.

Now, writing ratio of area of circle A and B, to find the ratio of radius.

⇒$\frac{\pi r_1^{2} }{\pi r_2^{2} } = \frac{36\pi }{64\pi }$

Cancelling out the common factor

⇒ $\frac{r_1^{2} }{r_2^{2} } = \frac{36 }{64}$

⇒ $(\frac{r_1 }{r_2} )^{2} = \frac{36 }{64}$

Taking square on both side.

Remember; √a²= a

⇒ $(\frac{r_1 }{r_2} ) =\sqrt{ \frac{36 }{64}}$

⇒ $(\frac{r_1 }{r_2} ) = \frac{6}{8}$

⇒$\frac{r_1 }{r_2} = \frac{3}{4}$

Hence, ratio of the radius of circle A to the radius of circle B is 3:4 or 3/4.