# Circle

The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r2, where r is the circle’s radius, is the formula for calculating a circle’s surface area. The square unit—for instance, m2, cm2, in2, etc.—is the unit of area.

For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. A circle does it have volume? The answer is no, a circle lacks volume. a sphere

**What is the Area of Circle?**

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle. It may also be referred to as the total number of square units inside that circle. **Area of Circle = πr ^{2} or πd^{2}/4 in square units, where**

- (Pi) π
**=**22/7 or 3.14. - r = radius of the circle
- d = diameter of the circle

Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.

**Circle and Parts of a Circle**

Before studying about the area of a circle in more detail, let’s review the circle and its components. A circle is made up of a group of points that are spaced uniformly apart from its centre. A closed geometric shape is a circle. Everyday objects like wheels, pizzas, round earth, etc. are circles. The area of the circle is the measurement of the area contained within the circle.

**Centre: **The radius of a circle is the distance from the centre to a point on the edge. The letter ‘r’ or ‘R’ stands in for it. We will discover later that the radius is crucial in the formula for the area and circumference of a circle.

**Diameter: **A circle’s diameter is defined as a line whose endpoints are on the circle and which passes through its centre. The letter ‘d’ or ‘D’ stands in for it.

**Circle diameter formula:** A circle’s diameter is equal to twice its radius. Radius divided by two equals the diameter. D is equal to 2R or D. If a circle’s diameter is known, its radius.

The following formula can be used to get the circumference:puted using the formula r = d/2 or R = D/2

**Circumference:** The length of a circle’s boundary determines its circumference. As a result, a circle’s circumference is sometimes referred to as its perimeter. The circumference of the circle will be equal to the length of the rope that precisely encircles its edge. You can see the same using the figure below.

**Surface Area of Circle**

A circle is nothing more than a sphere’s two-dimensional depiction. The circle’s surface area is equal to the whole area that is included inside the circle’s perimeter. When we say that we need the circle’s area, what we really mean is the circle’s surface area. In some cases, a circle’s area is also defined by its volume.

We can use the surface formula to determine the surface area when the radius, diameter, or even circle’s circumference is already known. Square units are used to indicate the surface.

A = x r2 is the formula for the circle’s surface area.

**How to Find Area of a Circle?**

As is common knowledge, a circle’s area is equal to pi times the square of its radius, or x r2. We need to know the circle’s radius or diameter in order to calculate its area.

For instance, if a circle has a radius of 7 cm, its area will be as follows: area of circle with radius of 7 cm = r2 = (7)2 = 22/7 x 7 x 7 = 22 x 7 = 154 sq. cm.

Additionally, we can determine the circle’s area if we know its circumference.

How?

As a result, the circumference is equal to the product of the circle’s radius and pi, or C = 2r.

As a result, r = C/2 is the radius value that can be found here.

Once the value of radius has been assessed.

**Difference Between Square Area and Circle Area**

When the circle’s diameter and the square’s side length are equal, the area of a circle is thought to be 80% of the area of a square.

Another exercise that students might complete is to place a circular object into a square shape that has the same diameter and side length.

If the area of a square is 100 square units, the area of a circle will be about 80 square units.

**Question 1**

**Find the circumference and the area of circle if the radius is 5 cm.**

**Solution:**

Given: Radius, r = 5 cm

We know that the circumference/ perimeter of the circle is 2πr cm.

Now, substitute the radius value, we get

C = 2 × (22/7)× 5

C = 2×22/7×5

C = 31.4 cm

Thus, the circumference of the circle is 31.4 cm.

Now, the area of the circle is πr2 cm2

A = (22/7) × 5 × 5

A = 22/7 × 25

A = 78.57 cm2

**Question 2**

**If the longest chord of a circle is 18 cm, then find the area of circle.**

**Solution:**

Given that the longest chord of a circle is 18 cm.

We know that the longest chord of a circle is the diameter.

Hence, d = 18 cm.

So, r = d/2 = 18/2 = 9 cm.

The formula to calculate the area of circle is given by,

A = πr2 square units.

Now, substitute r = 9 cm in the formula, we get

A = (22/7)×9×9 cm2

A = (22/7)×81 cm2

A = 254.57 cm2 (Rounded to 2 decimal places)

Therefore the area of circle is 254.57 cm2.

**What does “area of circle” mean?**The region that a circle occupies in a two-dimensional space is known as the area of the circle.

**What is the circle’s perimeter?**The circumference of a circle, or its perimeter, is equal to the product of twice the radius of the circle and pi (), or 2r.

**How do you figure out a circle’s area?**The equation Area = x r2 in terms of radius ‘r’ can be used to determine the area of a circle.

Area is equal to (/4) x d2, where d is the diameter.

In terms of the circumference, “C,” area equals C2/4.