Question

Both circle Q and circle R have a central angle measuring 60°. The area of circle Q's sector is 9π m2, and the area of circle R's sector is 16π m2. Which is the ratio of the radius of circle Q to the radius of circle R?

Answer 1

The ratio of the radius of circle Q to the radius of circle R is
`(3)/(4)`

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

`z^(2)=(x)/(y)`

substitute

`z^(2)=(9\pi)/(16\pi)`

`z^(2)=(9)/(16)`

square root both sides

`z=(3)/(4)` ------> 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

`z=(x)/(y)`

therefore

`(x)/(y)=(3)/(4)`