Question

The circumferences of two circles are in the ratio 3 : 4. The ratio of their areas is ______.

Options

• 3 : 4

• 4 : 3

• 9 : 16

• 16 : 9

Answer 1

The circumferences of two circles are in the ratio 3 : 4. The ratio of their areas is 9 : 16.

Explanation:

Let the the radii of the two circles be r and R, the circumferences of the circles be c and C and the areas of the two circles be a and A.

Now,

`c/C = 3/4`

⇒ `(2pir)/(2piR) = 3/4`

⇒ `r/R = 3/4`

Now, the ratio between their areas is given by:

`a/A = (pir^2)/(piR^2)`

= `(r/R)^2`

= `(3/4)^2`

= `9/16`