Answer:
The ratio of the radius of circle A to the radius of circle B are 3:4.
Explanation:
Area of a circle is
[tex]Area =\dfrac{\theta}{360}\pi r^2[/tex]
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
[tex]Area =\dfrac{50}{360}\pi r_1^2[/tex]
Area of B's sector is
[tex]Area =\dfrac{50}{360}\pi r_2^2[/tex]
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
[tex]\dfrac{\frac{50}{360}\pi r_1^2}{\frac{50}{360}\pi r_2^2}=\dfrac{36\pi}{64\pi}[/tex]
Cancel out the common factors.
[tex]\dfrac{r_1^2}{r_2^2}=\dfrac{9}{16}[/tex]
[tex](\dfrac{r_1}{r_2})^2=\dfrac{9}{16}[/tex]
Taking square root on both sides.
[tex]\dfrac{r_1}{r_2}=\dfrac{3}{4}[/tex]
Therefore, the ratio of the radius of circle A to the radius of circle B are 3:4.
