Question

If the scale factor between two circles is 7a/9b what is the ratio of their areas?

A. 49a/81b
B. 49a2/81b2
C. 81b2/49a2
D. 81b/49a

Answer 1

. 49a2/81b2
I think the answer is B)

Answer 2

Answer: The correct option is (B)
`(49a^2)/(81b^2).`

Step-by-step explanation: Given that the scale factor between two circles is
`(7a)/(9b)`.

We are to find the ratio of the areas of the two circles.

Let r and R be the radii of the two circles and A and B be the corresponding areas.

We know that the scale factor is the ratio of the radii of the two circles.

So, we have

`(r)/(R)=(7a)/(9b)\\\\\\\Rightarrow (r^2)/(R^2)=(49a^2)/(81b^2)\\\\\\\Rightarrow (\pi r^2)/(\pi R^2)=(49a^2)/(81b^2)\\\\\\\Rightarrow (A)/(B)=(49a^2)/(81b^2).`

Thus, the required ratio of the areas of the two circles is
`(49a^2)/(81b^2).`

Option (B) is CORRECT.