## How to Find the Area and Circumference of Circles

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### Radius of a Circle

The **distance** going from the center to the outer line of a circle is known as the radius. It’s the top **vital** quantity of the circle depending on what **formulas** used for the area and circumference of the circle are taken. The **diameter** of a circle is **twice** its radius. A diameter **slices** a circle into \(2\) equal parts, and that is known as a **semi-circle.**

### Circle’s Circumference

The Circumference of a circle or the perimeter of a circle is the measurement of its **boundary.** Where the circle’s describes the region it occupied. If a circle is opened and you make it into a **straight line,** its **length** is its **circumference.** It’s normally measured in **units,** like centimeters or unit millimeters.

### Formula for the Circumference of a Circle

Circumference (or) perimeter of a circle \(= \ 2πR\)

when \(R\) is the **radius** of the circle, \(π\) is the mathematical **constant** with an approximate (up to two decimal points) value of \(3.14\)

For instance: If the circle’s radius is \(3\) centimeters, calculate the circumference.

Provided: **Radius** \(= \ 3\) centimeters, **Circumference** \(= \ 2πr \ = \ 2 \times 3.14 \times 3 \ = \ 18.84\) centimeters

### Formula for the Area of a Circle

The area of any circle is the area **encircled** by the circle itself or the area **enveloped** by it. To find the circle’s area use this formula: \(A \ = \ πr^2\)

When \(r\) is the circle’s **radius** of the circle, this formula can be applied to **every** circle with different radii.

### Circumference to Diameter

A circle’s diameter is **twice** the radius. The **proportion **in-between the circle’s **circumference** and its **diameter** equals the value of **Pi** (\(π\)). So, this means this proportion is the definition of the constant \(π\). (i.e) \(C \ = \ 2πr \ ⇒ \ C \ = \ πd\) (As, \(d \ = \ 2r\))

If one **divides** both sides by the circle’s diameter, you end up with a value that’s **approximately** close to the value of \(π\). So, \(\frac{C}{d} \ = \ π\).

### Exercises for Area and Circumference of Circles

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