The Difference Between Circumference and Diameter

The circumference of a circle is the distance around its outer edge, while the diameter is the distance across the circle passing through its center. The relationship between the circumference and diameter is defined by the mathematical constant π (pi), which is approximately equal to 3.14159. The formula to calculate the circumference of a circle is C = πd, where C represents the circumference and d represents the diameter.

Given Information

In this problem, we are given that the difference between the circumference and diameter of a circle is 150 meters. Let's analyze this information further to find the radius of the circle.

Calculating the Circumference

Let's assume that the radius of the circle is denoted by 'r'. The diameter of the circle can then be expressed as 2r (since the diameter is twice the radius). Using the formula for the circumference, we can say that C = π(2r) = 2πr.

Formulating the Equation

We are given that the difference between the circumference and diameter is 150 meters. Mathematically, this can be represented as:

2πr - 2r = 150

Simplifying the Equation

To solve for 'r', we can simplify the equation by factoring out 2r:

2r(π - 1) = 150

Now, we can isolate 'r' by dividing both sides of the equation by (π - 1):

r = 150 / (2(π - 1))

Calculating the Radius

Substituting the value of π as 22/7, we can calculate the radius:

r = 150 / (2(22/7 - 1))
r = 150 / (2(22/7 - 7/7))
r = 150 / (2(15/7))
r = 150 / (30/7)
r = 150 * (7/30)
r = 35

Therefore, the radius of the circle is 35 meters.

Conclusion

The correct answer is option 'B', which states that the radius of the circle is 35 meters. By using the given information and the formula for the circumference of a circle, we can solve for the radius and determine the correct answer.