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](https://tex.z-dn.net/?f=Area%20%3D%5Cdfrac%7B%5Ctheta%7D%7B360%7D%5Cpi%20r%5E2)
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](https://tex.z-dn.net/?f=Area%20%3D%5Cdfrac%7B50%7D%7B360%7D%5Cpi%20r_1%5E2)
Area of B's sector is
![Area =\dfrac{50}{360}\pi r_2^2](https://tex.z-dn.net/?f=Area%20%3D%5Cdfrac%7B50%7D%7B360%7D%5Cpi%20r_2%5E2)
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}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cfrac%7B50%7D%7B360%7D%5Cpi%20r_1%5E2%7D%7B%5Cfrac%7B50%7D%7B360%7D%5Cpi%20r_2%5E2%7D%3D%5Cdfrac%7B36%5Cpi%7D%7B64%5Cpi%7D)
Cancel out the common factors.
![\dfrac{r_1^2}{r_2^2}=\dfrac{9}{16}](https://tex.z-dn.net/?f=%5Cdfrac%7Br_1%5E2%7D%7Br_2%5E2%7D%3D%5Cdfrac%7B9%7D%7B16%7D)
![(\dfrac{r_1}{r_2})^2=\dfrac{9}{16}](https://tex.z-dn.net/?f=%28%5Cdfrac%7Br_1%7D%7Br_2%7D%29%5E2%3D%5Cdfrac%7B9%7D%7B16%7D)
Taking square root on both sides.
![\dfrac{r_1}{r_2}=\dfrac{3}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7Br_1%7D%7Br_2%7D%3D%5Cdfrac%7B3%7D%7B4%7D)
Therefore, the ratio of the radius of circle A to the radius of circle B are 3:4.