Given: circle where its area is increasing at a uniform rate
To prove perimeter varies inversely as the radius
Explanation: Let the radius of the circle be ‘r’.
Let A be the area of the circle,
Then A = πr2……..(i)
As per the given criteria the area is increasing at a uniform rate, then
Now substituting the value from equation (i) in above equation, we get
Now let P be the perimeter of the circle, then
P = 2πr
Now differentiating perimeter with respect to t, we get
Now substituting value from equation (ii) in the above equation we get
Hence the perimeter of the circle with given condition varies inversely as the radius.
Hence Proved