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The circumference of a circle of diameter D is πD.
Since π is a constant, the circumference of circle is directly proportional to the diameter of the circle. If we change the diameter by k times, then the circumference will change by k times.

For example, consider a circle with diameter 7 cm.
circumference =  πD = (22/7)× 7 = 22cm
now make diameter twice or D = 2×7 = 14cm
new circumference = πD = (22/7)×14 = 44cm which is twice of previous circumference. So the circumference also became twice when diameter became twice.
Diameter= \pi  x^{2}  
where x is redius ,and when we x mean 2x then the result is 2 \pi  x^{2} *2.
example:-a circle with redius 4 m then circumference is =2 \pi 16=100.48 and if we double then it is 8 m redius then circumference is=2 \pi 64=401.92