The circumference of a circle exceeds its diameter by 45 cm. Find the circumference of the circle.

Given, the circumference of a circle exceeds its diameter by 45 cm.


Circumference of circle = Diameter of circle + 45


Let ‘d’ = diameter of the circle


Circumference = d + 45 eqn1


And we know, Circumference of a circle = 2πr eqn2


Where r = radius of circle


Also, we know that the radius of the circle is half of its diameter.



Put value of circumference in equation 1 from equation 2


2πr = d + 45 eqn4


Put value of r in equation 4 from equation 3



πd = d + 45


πd – d = 45


(π – 1)d = 45 (taking d common from L.H.S)






On rearranging, we get




d = 21 cm


Therefore, the diameter of the circle is 21 cm.


Thus, the radius of the circle



r = 10.5 cm


Now put the value of r in equation 2, we get






= 66 cm


The circumference of the circle is 66 cm.


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