Math Problem Statement

The diameter of a circle is 34 m. Find the circumference to the nearest tenth.

Solution

To find the circumference of a circle, we use the formula:

C=πdC = \pi d

where:

  • CC is the circumference,
  • dd is the diameter of the circle.

Given:

  • The diameter d=34d = 34 meters.

Now, substituting the values:

C=π×34C = \pi \times 34

Using π3.1416\pi \approx 3.1416:

C3.1416×34=106.8144C \approx 3.1416 \times 34 = 106.8144

Rounding to the nearest tenth:

C106.8mC \approx 106.8 \, \text{m}

So, the circumference of the circle is approximately 106.8 meters.

Would you like any further details or have any questions? Here are a few related questions to explore:

  1. How does the formula for the circumference change if the radius is given instead of the diameter?
  2. What would the area of this circle be, given the same diameter?
  3. How can we derive the formula for the circumference using the radius instead of the diameter?
  4. How does the relationship between the diameter and the circumference help us understand π?
  5. What happens to the circumference if the diameter is doubled?

Tip: Remember that the circumference is proportional to the diameter, meaning that if the diameter increases, the circumference increases in direct proportion.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle
Circumference

Formulas

C = πd

Theorems

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Suitable Grade Level

Grades 6-8