What is minimum radius (> 1) of a circle whose circumference is an integer?

Correct option is C

Given:

Radius $$> 1$$​​

Solution:

Circumference of the circle = $$2\pi r$$​

For an integer, the value of   r  must be an integer multiple of   $$\frac{1}{\pi}$$​ .

Let $$r = \frac{x}{\pi}$$​, where x  is a positive integer.

But r > 1 , so:

$$\frac{x}{\pi} > 1$$  

$$x > \pi\\x > 3.14$$​

For minimum  r ,  x  must be minimum.

Since the least integer greater than $$\pi$$​  is 4, we get:
x = 4
The minimum value of r = $$\frac{4}{\pi}$$​