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 R's sector is 64π cm2. Which is the ratio of the radius of circle Q to the radius of circle R?

Answer 1

7/8π

The circles have the same central angle measures; therefore, the ratio of the intercepted arcs is the same as the ratio of the radii.

23 = 34πx
x = 98π

Answer 2

Answer:

The ratio of the radius of circle A to the radius of circle B are 3:4.

Explanation:

Area of a circle is

$Area =\dfrac{\theta}{360}\pi r^2$

Let radius of circle A and circle B are r₁ and r₂ receptively.

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

Area of A's sector is

$Area =\dfrac{50}{360}\pi r_1^2$

Area of B's sector is

$Area =\dfrac{50}{360}\pi r_2^2$

The area of circle A's sector is 36π cm2, and the area of circle R's sector is 64π cm2. So, the ratio of area is

$\dfrac{\frac{50}{360}\pi r_1^2}{\frac{50}{360}\pi r_2^2}=\dfrac{36\pi}{64\pi}$

Cancel out the common factors.

$\dfrac{r_1^2}{r_2^2}=\dfrac{9}{16}$

$(\dfrac{r_1}{r_2})^2=\dfrac{9}{16}$

Taking square root on both sides.

$\dfrac{r_1}{r_2}=\dfrac{3}{4}$

Therefore, the ratio of the radius of circle A to the radius of circle B are 3:4.