Math Problem Statement

If a circle has a diameter of 10 meters, what is its circumference?

a.

20 meters

b.

30 meters

c.

31.4 meters

d.

40 meters

Solution

The circumference of a circle can be calculated using the formula:

C=πdC = \pi \cdot d

where dd is the diameter of the circle and π3.14\pi \approx 3.14. Given the diameter d=10d = 10 meters:

C=π103.1410=31.4metersC = \pi \cdot 10 \approx 3.14 \cdot 10 = 31.4 \, \text{meters}

Thus, the correct answer is:

c. 31.4 meters

Would you like a more detailed explanation or have other questions about this? Here are five related questions to expand your understanding:

  1. How would the formula change if you were given the radius instead of the diameter?
  2. What is the relationship between diameter and radius?
  3. How can you calculate the area of a circle with the same diameter?
  4. If the diameter were doubled, what would happen to the circumference?
  5. How is π\pi derived and why is it used in circle formulas?

Tip: Remember, the diameter is always twice the radius (d=2rd = 2r).

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle properties
Circumference calculation

Formulas

Circumference formula: C = π × d

Theorems

Relationship between diameter and radius (d = 2r)
Constant value of π

Suitable Grade Level

Grades 6-8