Area of Segment Formula Class 10
Area of segment formula class 10 enables us to calculate the area formed between the arc and the chord of a circle. This area is known as the area of a segment of a circle. To compute this area we make use of the two endpoints of the chord which meet the periphery of the circle. Let's assume a chord meets the circle in points A and B, now if we connect the two endpoints A and B to the center 'O' of the circle then the angle AOB gives us a measure of the fraction of the circle that is segmented by the chord. This fraction of circle is called sector and the bigger the angle, the bigger is the size of the sector.
To help students learn this in a simple and easy way this article presents the concepts of area of segment formula class 10 in a concise manner. Students will also find some handy tips to remember these formulas towards the end of this article.
List of Area of Segment Formula Class 10
Here is a list of area of segment formula class 10:
- Area of a Segment in Radians = A = (½) × r2 (θ – Sin θ)
- Area of a Segment in Degrees = A = (½) × r2 × [(π/180) θ – sin θ]
- Area of the sector of angle θ = (θ/360) × π r2
- Length of an arc of a sector of angle θ = (θ/360) × 2π r
Applications of Area of Segment Formula Class 10
Area of segment formula has its widespread use in our everyday lives. Some of the practical applications of area of segment formula class 10 are listed below:
- Area of segment formula is useful in scenarios where only a particular area of a circle needs to be determined. For example, the area of the sea over which the lighthouse spans its light to signal ships.
- It is also applied when only a certain part of a circular plot needs construction or some modification.
Tips to Memorize Area of Segment Formula Class 10
To help students remember the area of segment formula class 10 with ease below are some important tips:
- Area of segment can be derived by subtracting the area of the triangle from the area of the sector( which itself gets derived from the area of the circle). Thus, attaining a clear understanding of the area of circle, sector and other relevant terms is vital to memorize these formulas.
- Students should plan revision and practice with some interactive resources like formula sheets and assessments tests available on internet. It will help them revise it better.
- They can set the formula images as wallpaper on their mobile devices and laptops to refresh them in their memory.
Area of Segment Formula Class 10 Examples
Example 1: In a circular football field students have decided to host a school fair. They can use only 20 sq meters of the football field as per the school management. Thus, students drew a 14 meters line cutting the field in two portions and took the minor segment for setting up the fair.
If the radius of the field is 14 meters then can you tell if the students are taking more or less than the allocated area?
Solution: Area of the field = pi × radius × radius
=22/7 × 14 × 14 = 616 square meter
Area of segment = Area of sector - Area of triangle
As all sides of the triangle are equal (14 meters) the angle made at the center = 60°
So, Area of sector = 60/360 × area of circle
= 1/6 × 616 = 103 sq meters
Area of triangle with length of side = 14 meters = 3/4 × 14 × 14 = 85 square meters
Area of segment = 103 - 85 = 18 sq meters.
Thus students are using less than 20 square meters for the fair.
Example 2: Arvind bought a pizza of radius 28 inches and then cut it into 4 identical sector slices. Arvind’s daughter prefers to eat the crust so Arvind cut each sector using a chord and created segments. Determine the amount of pizza Arvind’s daughter gets?
Solution: Area of each slice of pizza = 1/4 × Area of a full pizza
Area of full pizza = 22/7 × 28 × 28
= 2464 sq inches
Area of each slice = 2464/4 = 616 square inches.
Area of segment = Area of slice - Area of the triangle
By applying the formula of area of isosceles right-angle triangle = 1/2 × 28 × 28 = 392 sq inches
Area of segment = 616 - 392 = 224 square inches
Total area of four segments = 224 × 4
= 896 square inches
Students can download the printable Maths Formulas Class 10 sheet from below.
FAQs on Area of Segment Formula Class 10
What are the Important Formulas Covered Under Area of Segment Formula Class 10?
The important area of segment formula class 10 with explanation can be found in this article. Some of the important ones are listed below:
- Area of Segment = Area of Sector - Area of Triangle AOB
- Area of the Sector of angle θ = (θ/360) × π r2
- Length of an arc of a Sector of angle θ = (θ/360) × 2π r
What are the Benefits of Memorizing Area of Segment Formula Class 10?
Memorizing area of segment class 10 formulas listed in this article will help students to understand the definitions of sector and segment in a circle. It will also enable them to determine the measure of the fraction of the circle that is segmented by the chord. These formulas explain the ratio of Area of circle and Area of the sector.
Why is it Important to Solve Problems Based on Area of Segment Formula Class 10?
Solving problems based on area of segment formula class 10 is useful for students to learn how to determine the area of the segment based on the angle made by the sector at the center of the circle. By practicing the questions related to area of segment formula students will form a clear understanding of concepts and terms associated with this topic.
How Many Formulas are There in the Area of Segment Formula Class 10?
There are three major formulas in area of segment formula class 10. Area of sector and perimeter of sector are important formulas that can be derived using the circle formulas. Also, the area of the segment can be obtained by finding the area of the sector minus the area of the inscribed triangle.
How can I Memorize the Area of Segment Formula Class 10?
Students can memorize area of segment formula class 10 with the help of the tips mentioned in this article. Here are a few of them:
- The students are advised to first go through the basic formula related terms and their definitions.
- Writing formulas with their explanations is also one of the best ways to understand them better.
- Students can take help of formula images by setting them as wallpaper on their mobile devices and laptops.