Math Problem Statement

Find the circumference of the circle. The radius is 6 yards. Leave your answer in terms of π.

Solution

The problem asks for the circumference of a circle, where the radius is given as 6yd6 \, \text{yd}.

The formula for the circumference CC of a circle is:

C=2πrC = 2\pi r

Where rr is the radius of the circle. Substituting r=6ydr = 6 \, \text{yd}:

C=2π×6=12πydC = 2\pi \times 6 = 12\pi \, \text{yd}

Thus, the circumference is 12πyd12\pi \, \text{yd}.

Would you like further details or have any questions?

Here are some related questions you might explore:

  1. What is the area of the circle with the same radius of 6 yards?
  2. How does the circumference change if the radius is doubled?
  3. How would you calculate the diameter of the circle using the given radius?
  4. If the radius is given in meters, how would you convert it to yards before calculating the circumference?
  5. How would the formula for circumference change for an ellipse?

Tip: Always ensure you're using the correct units for radius or diameter before applying formulas for circumference.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circumference of a Circle

Formulas

C = 2πr

Theorems

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Suitable Grade Level

Grades 6-8