Answer:
The ratio of the radius of circle Q to the radius of circle R is [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
In this problem
Let
z-----> the scale factor
x-----> the area of circle Q's sector
y-----> the area of circle R's sector
so
[tex]z^{2}=\frac{x}{y}[/tex]
substitute
[tex]z^{2}=\frac{9\pi}{16\pi}[/tex]
[tex]z^{2}=\frac{9}{16}[/tex]
square root both sides
[tex]z=\frac{3}{4}[/tex] ------> scale factor
step 2
Find the the ratio of the radius of circle Q to the radius of circle R
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
In this problem
The ratio of its corresponding radius is equal to the scale factor
so
Let
z------> the scale factor
x-----> the radius of circle Q
y-----> the radius of circle R
so
[tex]z=\frac{x}{y}[/tex]
therefore
[tex]\frac{x}{y}=\frac{3}{4}[/tex]
