The ratio of the radii of two circles is 1 : 4. The ratio of their areas is:

Correct option is D

Given:

The ratio of radii of two circles = 1 : 4

Formula used:

Area of circle = ​πr²​

Solution:

Let, 

The given radii be r1 : r2 = 1 : 4

The area of two circle be A1 : A2

Now,

$$\dfrac{A1}{A2}=$$ $$\dfrac{π(r1)^2}{π(r2)^ 2}$$

$$\dfrac{A1}{A2}=\dfrac{(r1)^2}{(r2)^ 2}$$

$$\dfrac{(r1)^2}{(r2)^ 2}=(\dfrac{1}{4})^2 =\dfrac{1}{16}$$

Therefore, the ratio of their area is 1 : 16.

Thus, Option D is correct.