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Bunuel
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Radius = r
new radius = r+x

Earlier Circumference: 2πr
New Circumference: 2π(r+x)

New change : 2π(r+x) - 2πr = 2πx

IMO-D
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Bunuel
If x units are added to the length of the radius of a circle, what is the number of units by which the circumference of the circle is increased?

A. x
B. 2
C. 2π
D. 2πx
E. x^2

let the initial radius of the circle be r
hence circumference = 2πr

now, x units are added to the radius = r+x
hence circumference =2π(r+x)=2πr+2πx

hence, Answer D
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