Math Problem Statement

For a circle of radius r, the ratio of the circumference to the diameter is

Solution

This problem asks about the ratio of the circumference of a circle to its diameter when the radius is given as rr.

The formula for the circumference CC of a circle is: C=2πrC = 2\pi r

The diameter DD of a circle is: D=2rD = 2r

To find the ratio of the circumference to the diameter, we divide the circumference by the diameter: Ratio=CD=2πr2r=π\text{Ratio} = \frac{C}{D} = \frac{2\pi r}{2r} = \pi

So, the correct answer is:

(B) π\pi.

Would you like further details or have any questions on this? Here are some related questions:

  1. What is the relationship between the radius and the circumference of a circle?
  2. How is the diameter of a circle related to its radius?
  3. What is the formula for the area of a circle?
  4. How do you derive the formula for the circumference of a circle?
  5. What is the significance of π\pi in circle-related formulas?

Tip: Remember that in any circle, the ratio of the circumference to the diameter is always π\pi, which is approximately 3.1416.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circles
Ratios

Formulas

Circumference formula: C = 2πr
Diameter formula: D = 2r

Theorems

The ratio of the circumference to the diameter of any circle is π

Suitable Grade Level

Grades 6-8