SOLUTION: The circumference of a circle exceeds its diameter by 30 cm.Find the radius of the circle

Question 549727: The circumference of a circle exceeds its diameter by 30 cm.Find the radius of the circle
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
c = circumference of a circle = 2 * pi * r
d = diameter of a circle = 2 * r
r = the radius of the circle
the circumference of a circle exceeds its diameter by 30 cm.
this means that:
c = d + 30
substituting for c and d, we get:
2 * pi * r = 2 * r + 30
subtract 2 * r from both sides of the equation to get:
(2 * pi * r) - (2 * r) = 30
factor out the (2 * r) on the left side of the equation to get:
(2 * r) * (pi - 1) = 30
divide both sides of this equation by (pi - 1) to get:
2 * r = 30 / (pi - 1)
divide both sides of this equation by 2 to get:
r = 30 / ((pi - 1) * (2))
solve to get:
r = 7.004133104
this means that:
d = 7.004133104 * 2 = 14.00826621
the circumference of the circle is equal to 2 * pi * r which is equal to 2 * pi * 7.004133104 which is equal to 44.00826621.
the difference between the circumference and the diameter is equal to 44.00826621 - 14.00826621 = 30.

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