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what is the area of circle if the cirucmference 22pi

what is the area of circle if the cirucmference 22pi

less than a minute read 21-01-2025
what is the area of circle if the cirucmference 22pi

Knowing the circumference of a circle allows you to easily calculate its area. This article will walk you through the steps, providing a clear and concise explanation of how to solve this common geometry problem. We'll also explore the underlying formulas and concepts.

Understanding the Formulas

To solve this, we need two key formulas relating to circles:

  • Circumference (C): C = 2πr (where 'r' is the radius)
  • Area (A): A = πr² (where 'r' is the radius)

Notice that both formulas rely on the radius (r). Therefore, to find the area, we first need to determine the radius using the given circumference.

Calculating the Radius

We're given that the circumference is 22π. Let's plug this into the circumference formula and solve for 'r':

22π = 2πr

Divide both sides by 2π:

r = 11

Therefore, the radius of the circle is 11 units.

Calculating the Area

Now that we know the radius, we can calculate the area using the area formula:

A = πr² = π(11)² = 121π

Therefore, the area of the circle is 121π square units.

Different Units & Practical Applications

Remember that the units for the area will be square units (e.g., square centimeters, square meters, etc.), reflecting that we're measuring a two-dimensional space. The exact numerical value depends on the unit of measurement used for the circumference. If the circumference was given in centimeters, the area would be 121π square centimeters.

Understanding how to calculate the area of a circle from its circumference is useful in various fields:

  • Engineering: Designing circular components, calculating material requirements.
  • Architecture: Designing circular features in buildings, calculating space.
  • Real Estate: Determining the area of circular plots of land.
  • Cartography: Calculating areas on maps using circular approximations.

Summary: Area of a Circle from Circumference

To recap, given a circumference of 22π, we found the radius to be 11 units. Using this radius in the area formula, we determined that the area of the circle is 121π square units. This simple process highlights the interconnectedness of key geometric properties of circles.

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