Respuesta :
Answer:
D) 9 : 16
Step-by-step explanation:
Given,
Central angle for circle Q = Central angle for circle R = 75°
Ratio of the radii of circle Q to circle R = [tex]\frac{3}{4}[/tex]
We have to find the ratio of the areas of the sector for circle Q to the sector for circle R.
Solution,
Since we know that the formula for Area of sector is [tex]\frac{\pi r^2\theta}{360}[/tex].
So the ratio of the areas of sectors for circle Q to circle R;
[tex]Ratio=\frac{\frac{\pi r_1^2\theta}{360}}{\frac{\pi r_2^2\theta}{360}}[/tex]
Here the central angle(θ) is equal for both circles.
And also π and 360° is equal, so we can cancel it.
Now,
[tex]Ratio = \frac{r_1^2}{r_2^2}[/tex]
Since the ratio of the radii of circle Q to circle R = [tex]\frac{3}{4}[/tex]
We can also say that [tex]\frac{r_1}{r_2}=\frac{3}{4}[/tex]
Now we substitute the value of [tex]\frac{r_1}{r_2}[/tex] and get;
[tex]Ratio=(\frac{3}{4})^2=\frac{3^2}{4^2}=\frac{9}{16}[/tex]
Hence The ratio of the area of the sector for circle Q to the area of the sector for circle R is 9:16.
