Math Problem Statement

Find the circumference of the circle with a radius of 6 units. Round your answer to the nearest hundredth.

Solution

To find the circumference of the circle, we use the formula for the circumference CC of a circle, which is given by:

C=2πrC = 2\pi r

Where:

  • rr is the radius of the circle.
  • π\pi is approximately 3.141593.14159.

From the image, the radius rr of the circle is 6 units.

Now, let's calculate the circumference:

C=2π×6C = 2 \pi \times 6 C2×3.14159×6=37.69908C \approx 2 \times 3.14159 \times 6 = 37.69908

Rounded to the nearest hundredth, the circumference is approximately:

C37.70unitsC \approx 37.70 \, \text{units}

Would you like further explanation or have any questions?

Here are 5 related questions to explore further:

  1. What is the formula for the area of a circle, and how does it relate to the radius?
  2. How would the circumference change if the radius doubled?
  3. What is the difference between the circumference and the diameter of a circle?
  4. How is the concept of a circle’s circumference applied in real-life situations?
  5. What is the relationship between the circumference and the arc length of a circle?

Tip: When solving geometry problems, always ensure you correctly identify whether you're given the radius or diameter, as it significantly affects your calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle
Circumference

Formulas

C = 2 * π * r

Theorems

Theorem: The circumference of a circle is proportional to its radius, given by the formula C = 2πr

Suitable Grade Level

Grades 6-8