The Circumference of a Circle Exceeds its Diameter by 30 cm: Finding the Radius

To find the radius of a circle when the circumference exceeds the diameter by 30 cm, we need to understand the relationship between the circumference, diameter, and radius of a circle. Let's break down the problem step by step.

Understanding the Terms:
- Circumference: The circumference of a circle is the distance around its outer edge.
- Diameter: The diameter of a circle is a straight line passing through the center and touching two points on the circumference, effectively dividing the circle into two equal halves.
- Radius: The radius of a circle is the distance from the center to any point on the circumference.

Formulas:
- The circumference of a circle is given by the formula: C = 2πr, where "C" represents the circumference and "r" represents the radius.
- The diameter of a circle is twice the radius: D = 2r.

Given Information:
The problem states that the circumference exceeds the diameter by 30 cm. Mathematically, this can be expressed as: C - D = 30 cm.

Using Formulas to Solve the Problem:
1. Substitute the formulas for circumference (C) and diameter (D) into the given information equation: 2πr - 2r = 30 cm.
2. Simplify the equation by factoring out the common term "2r": 2r(π - 1) = 30 cm.
3. Divide both sides of the equation by (π - 1) to isolate the radius (r): r = 30 cm / (2(π - 1)).
4. Use an approximation for π, such as 3.14, to calculate the value of the radius.

Calculating the Radius:
Let's substitute the approximate value of π into the equation and solve for the radius:

r = 30 cm / (2(3.14 - 1))
r = 30 cm / (2(2.14))
r ≈ 30 cm / 4.28
r ≈ 7.01 cm (rounded to two decimal places)

Therefore, the radius of the circle is approximately 7.01 cm.