Area of a Circle
Class 10 Maths Circles is an important part of this syllabus. Students will develop their concepts related to this closed geometric figure and its various parts by understanding and memorising its formulas. To make it easier, focus on how the subject experts of Vedantu have explained the circle formulas in simpler language and take a step ahead with your preparation.
Class 10 Maths Circle Formulas Overview
The area of a circle can be considered as the number of square units of space the circle occupies.
For example, if you draw a square of 2 cm by cm inside the circle, then the total number of squares placed inside the circle represents the area of a circle. The units in which the area of the circle can be measured are m², km², in², mm², etc.
Let us learn important circle formulas through this article.
Area of a Circle Formulas
The area of circle formula in terms of the radius is given as:
The area of circle formula in terms of diameter is given as:
In the above area of circle formulas, ris the radius and d of the circle.
The value of \[\pi\] is \[\frac{22}{7}\] or 3.14.
Surface Area of Circle Formula
The surface area of a circle is defined as the total area occupied by the circle. The surface area of circle formula is given as:
What is a Circle?
A circle is defined as the set of all points in the plane that maintains a fixed finite distance (r) from a fixed centre point (x,y). Here, r is the radius and O is the centre point of a circle.
Equation of a Circle
The equation of a circle has two forms. These are:
The general form of the circle.
The standard form of the circle.
If the equation of a circle is given in the standard form, we can easily identify the coordinates of a centre and radius (r) of a circle. It should be noted that the radius (r) is always positive.
General Equation of a Circle
The general equation of a circle with coordinates of a centre (h,k), and radius r is given as:
Standard Equation of a Circle
The standard equation of a circle provides appropriate information about the centre point and radius of a circle and is, therefore, can be written and read easily.
The standard equation of a circle with centre (a,b), and radius r is given as:
A unique circle with centre point O = (a, b), and radius r can be constructed as shown below:
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Radius of a Circle Formula
The radius of a circle is the length of a line segment from the centre point of a circle to any point on its circumference. It is represented by “r”.
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The radius of a circle formula in terms of diameter is given as:
The radius of a circle formula in terms of the circumference is given as:
If the area of a circle is represented by A, then the radius of a circle formula in terms of area is given as:
Diameter of a Circle Formula
The diameter of a circle is defined as the length of a line that starts from one point on the circle, passes through the centre, and ends on the other point on the circle's opposite side.
The diameter of a circle formula is given as :
Circumference of Circle Formula
The circumference of a circle is the boundary or length of the complete arc of a circle.
The circumference of a circle formula is given as:
In the circumference of a circle formula, ris the radius of the circle and the value of π is 22/7 or 3.14.
Solved Examples
1. Find the area, circumference, and diameter of a circle of radius 5 cm.
Solution:
Area of a circle = π × r²
Here, r = 5 cm, π = 3.14
Area of a circle = 3.14 × 5² = 78.5 cm
Circumference of a circle = 2πr
Here, r = 5 cm, π = 3.14
Circumference of a circle = 2 × 3.14 × 5 = 31.4 cm
Diameter of a circle = 2 × radius
Here, r = 5 cm,
Diameter of a circle = 2 × 5 = 10 cm
2. What will be the equation of the circle whose centre is (2,6) and the radius is 4 units.
Solution:
Here, the centre of the circle is not an origin. Hence, the general equation of the circle will be applied.
The general equation of a circle = (x – x₁)² + (y – y₁)² = r²
Substituting the values:
(x - 2)² + (y - 6)² = 4²
Hence, the required equation of a circle is (x - 2)² + (y - 6)² = 4²
Importance of CBSE Class 10 Maths Circle Formulas
Learning what a circle is and how to derive the formulas related to its radius, diameter, circumference, area, etc are a part of the conceptual development process for the students of Class 10.
To make it easier, the subject experts of Vedantu have compiled the meaning and definition of the terms related to a circle. They have also discussed and derived the specific formulas related to this topic of Class 10 Maths to help students comprehend the concepts faster.
By referring to the precise notes based on the circle formulas, students will be able to study and recall the fundamental principles of this topic. Learning these formulas will aid students to proceed with the advanced chapters related to circles in the Class 10 Maths syllabus.
Benefits of learning Class 10 Maths Circles Formulas
The consolidated presentation of the formulas with descriptions will enable you to memorise, revise and recall them faster. You will enjoy the added advantage of accessing these formulas here along with some solved examples.
Find out the specific use of the terms in these formulas and learn how to use them. Make your conceptual foundation stronger by using the simpler depiction of the formulas.
Focus on how to use these formulas to solve fundamental problems related to circles. Proceed with your preparation by keeping these formulas handy.
Download CBSE Class 10 Maths Circle Formulas
Find the simpler explanation of the circle formulas here and make your preparation sessions more productive. Refer to these formulas whenever you want to solve geometric and mensuration problems related to circles. Use this page to memorise and revise the formulas faster before an exam and gain confidence. Utilise this confidence to solve problems and ace the exams.
Conclusion
With these circle formulas, you will be easily able to solve different questions based on the equation of a circle, area of a circle, the diameter of a circle, the radius of a circle, and circumference. So, understand the concepts behind the formula and apply them wherever required.
FAQs on Circle Formulas
Q1. How to Calculate the Distance Around the Boundary of a Circle?
The distance around the boundary of a circle can be calculated using the circumference of a circle formula.
Q2. What are the Real-Life Examples of a Circle?
Two typical examples of a circle that you find in real -life is:
Ferris Wheel - Each point located along the outer rim of the wheel is equidistant from the centre.
Bicycle Wheel - Bicycle wheels are the best example of a circle. The circle shape is considered to be a feasible shape for a bicycle as they roll very easily because they are round in shape.
Q3. What are the Two Different Forms of an Equation of a Circle?
Two different forms of an equation of a circle are:
The general form
The standard form
Q4. How can I understand the circle formulas for Class 10?
Focus on the terms used to make such formulas. Derive them stepwise as described in the chapter. Learn to use them by solving exercises and important questions designed by Vedantu. Apply them more to understand the circle formulas better
Q5. What is the best way to prepare for Class 10 Circles?
Study the theoretical portion of this chapter first. Proceed to solve the exercise of each section consecutively. Once the chapter is done, test your skills by solving the important questions set by the Vedantu experts to find out your preparation level. Repeat studying the same chapter and learn the concepts perfectly.