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.