A circle is a closed figure defined by a set of points equidistant from a fixed point called the centre. The distance between the centre and any point on the circle is called the radius, and the distance across the circle through the centre is called the diameter.

In geometrical language, **a circle is defined as a set of points in a plane at equal distances from a fixed point called the centre.** For example, imagine a Ferris wheel with people seated in each compartment. As the wheel rotates, each person moves in a circular path that is equidistant from the centre of the wheel. The distance from the centre of the Ferris wheel to any of its compartments is the circle's radius, and the distance around the circle is its circumference.

Suppose the Ferris wheel has a radius of 10 meters. To find its **circumference,** we can use the formula **C = 2πr,** where **r** is the radius of the circle and **π** is a constant approximately equal to 3.14159. Plugging in the values, we get:

Therefore, the circumference of the Ferris wheel is approximately 62.83 meters.

So, a circle is a set of points equidistant from a fixed point called the centre. The **distance from the centre to any point on the circle is the radius, and the distance around the circle is its circumference.** We can use the **formulas C = 2πr and A = πr ^{2} to calculate the circumference and area of a circle,** respectively.

## Calculating the circumference

The circumference of a circle is the distance around the circle, and the formula gives it:

**C = 2πr**

where C is the circumference, r is the radius, and π (pi) is a constant approximately equal to 3.14159.

The area of a circle is the amount of space inside the circle, and the formula gives it:

**A = πr**

^{2}where A is the area and r is the radius.

Here are some examples of how to use these formulas:

**Find the circumference and area of a circle with a radius of 5 cm.**

C = 2πr = 2π(5) = 10π ≈ 31.42 cm

A = πr^{2} = π(5^{2}) = 25π ≈ 78.54 cm^{2}

Therefore, the circle's circumference is approximately 31.42 cm, and the area of the circle is approximately 78.54 cm^{2}.

**Find the radius of a circle with a circumference of 25π cm.**

C = 2πr

25π = 2πr

r = 25π / 2π

r = 12.5 cm

Therefore, the radius of the circle is 12.5 cm.

**Find the diameter of a circle with an area of 36π cm**

^{2}.A = πr^{2}

36π = πr^{2}

r^{2} = 36

r = 6 cm

The radius of the circle is 6 cm, so the diameter is twice the radius:

d = 2r = 2(6) = 12 cm

Therefore, the diameter of the circle is 12 cm.

In summary, to find the circumference of a circle, we use the formula C = 2πr, where r is the radius. To find the area of a circle, we use the formula A = πr^2^. These formulas can be used to solve problems involving circles, such as finding the circumference, area, radius, or diameter of a given circle.

## Eating the Pi

Circles have unique characteristics that are essential to understand their relationships. These characteristics have specific terms associated with them that are important to recognise. One of the most important terms associated with circles is **=="pi" - a mathematical constant that represents the ratio of the circumference of a circle to its diameter.** Pi is an irrational number that has an infinite number of decimal places.

To **calculate pi, one can measure the diameter (d) and the circumference (C) of several circular objects and divide C by d. The result of this calculation should consistently be a number slightly over 3.** This number is the approximation of pi.

In any circle, pi is the circumference-to-diameter ratio. It is a constant with many applications in mathematics, including geometry, trigonometry, calculus, and physics.

In summary, Pi is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. By measuring the diameter and circumference of a circle, we can calculate pi as the ratio of the two values. Pi is an essential constant in mathematics and has various applications across many disciplines.

## Circles Revision Quiz

To answer the questions correctly, **hover over each option and click to select it.** After you finish, click **'Submit'** to check your **score and see the correct answers and explanations.** Most questions will include an **explanation with the answer.** Please take the time to read the explanations accompanying the answers to your questions. Doing so will **give you a better overall understanding of the topic.** All the best!

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