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Areas related to circles allow students to calculate the exact space enclosed by circular shapes and their segments. Using radius, diameter, chord length, and arc measures, these formulas help determine the area of a full circle, sectors, segments, and rings. They also connect to real-world applications in geometry, construction, design, and physics, where precise measurements of circular regions are required. These concepts also support real-world applications in geometry, construction, design, and physics and are commonly practised through structured Class 10 online CBSE maths tuition. In this blog, you will get to know the key formulas for areas related to circles in Class 10 Maths and learn how to apply each one effectively. Areas Related to Circles – Class 10 Maths Formulas Understanding areas related to circles helps calculate spaces, lengths, and segments in circular shapes accurately. These formulas are essential in CBSE Class 10 Maths for solving questions on full circles, sectors, segments, rings, and combinations of circular regions. They are widely applied in construction, design, sports fields, and real-life measurement problems where precision is required. Core Formulas for Areas and Circumference of a Circle Students can use the following key formulas related to circles in Class 10 for quick reference and practice: Circumference of a circle = 2πr Area enclosed by a circle = πr² Length of an arc of a sector with radius r and central angle θ = (θ / 360) × 2πr Area of a sector with radius r and angle θ = (θ / 360) × πr² Area of a segment of a circle = Area of the sector − Area of the triangle Read more: Complete Guide to Class 10 Maths Formulas Chapter by Chapter Practical Applications of Circle Area Formulas Read more: Quadratic Equations Formulas CBSE Class 10 Maths Tips to Master Areas Related to Circle Formulas Read more: Coordinate Geometry Class 10 Formulas with Solved Examples Area Related to Circle Class 10 – Solved Examples Example 1 A circular park has a boundary length of 220 m. The grass inside the park costs ₹5 per m² to maintain. Find the total maintenance cost of the park. Solution: Circumference of the park = 220 m Let the radius be r m 2πr = 220 r = 220 ÷ (2 × 3.14) r = 35 m Area of the park = πr²= 3.14 × 35²= 3846.5 m² Cost per m² = ₹5 Total maintenance cost = 3846.5 × 5= ₹19,232.50 Example 2 Two circular fields have radii 14 m and 21 m. Find the radius of a circle whose circumference is equal to the difference of the circumferences of the two fields. Solution: Circumference of first field= 2 × 3.14 × 14= 87.92 m Circumference of second field= 2 × 3.14 × 21= 131.88 m Difference of circumferences= 131.88 − 87.92= 43.96 m Let the required radius be R 2πR = 43.96 R = 43.96 ÷ (2 × 3.14) R = 7 m

A circle represents all points in a plane that lie at a fixed distance from a single point called the centre. This concept connects radius, diameter, chord, arc, and tangent through measurable relationships. In Class 10 Maths, circles help students analyze symmetry, angles, and length relationships using exact values rather than estimation. Circle based questions strengthen analytical reasoning and support related topics such as coordinate geometry, trigonometry, and mensuration, which are commonly reinforced through structured Class 10 online CBSE maths tuition. In this blog, you will learn the important circle formulas for CBSE Class 10 Maths and understand how each formula helps solve exam-based problems. List of Important Formulas for Circles Class 10 Maths Circle formulas help students calculate length, area, and portions of a circle using the radius and central angle. Each formula solves a specific type of problem commonly asked in CBSE Class 10 board exams. Basic Circle Measurements Read more: Complete Guide to Class 10 Maths Formulas Chapter by Chapter Formulas Related to Sectors and Arcs Read more: CBSE Class 10 Maths Trigonometry Formulas with Examples Formula for a Segment of a Circle Applications of Circle Formulas in Class 10 Maths Circle formulas help solve practical and academic problems that involve curved shapes and circular motion. These formulas connect radius, circumference, area, and angles in a measurable way. Read more: Quadratic Equations Formulas CBSE Class 10 Maths Tips to Learn and Remember Circle Formulas for Class 10 Learning circle formulas becomes easier when students focus on understanding instead of memorising. Read more: Coordinate Geometry Class 10 Formulas with Solved Examples Solved Examples Using Circle Formulas Example 1 Find the area of one-fourth of a circle when its perimeter measures 42 cm. Quadrant area = (π × radius²) ÷ 4Final answer = 35.02 cm² Example 2 A circle has a radius of 5 cm. An arc subtends 50 degrees at the centre. Find the arc length. Arc length = (50 ÷ 360) × 2 × 3.14 × 5Final answer = 4.36 cm

Quadratic equations for Class 10 form a fundamental part of the CBSE Mathematics curriculum and assess a student’s understanding of algebraic concepts. Through Class 10 online CBSE maths tuition, students practice solving second-degree polynomials, determine the nature of solutions, and tackle exam problems accurately. A clear understanding of how formulas work and how to apply them in different situations allows students to solve quadratic equations correctly and avoid common errors. In this blog, you will get to know the key quadratic equations formulas, how to use them to find roots, and how these formulas apply across different types of Class 10 problems. Important Quadratic Equations Formulas Class 10 Standard Form of a Quadratic Equation A quadratic equation represents a second-degree polynomial written as: ax² + bx + c = 0, where a ≠ 0 Here, a, b, and c are real numbers. The value of a controls the degree of the equation and confirms it as quadratic. Read more: Complete Guide to Class 10 Maths Formulas Chapter by Chapter Roots of a Quadratic Equation A real number α becomes a root of the equation ax² + bx + c = 0 when it satisfies the condition: aα² + bα + c = 0 If this equality holds true, then x = α solves the quadratic equation. Read more: CBSE Class 10 Maths Chapter 2 Polynomials Formula Methods Used to Solve Quadratic Equations Factorisation Method This method works when the quadratic expression splits into two linear factors. After factorisation, equate each factor to zero to find the roots. Best used when coefficients remain small and factor pairs exist clearly. Completing the Square Method This approach converts a quadratic expression into a perfect square by rearranging terms. Key identities used: Quadratic Formula When the discriminant value stays zero or positive, the roots follow this formula: x = (−b ± √(b² − 4ac)) / 2a Read more: CBSE Class 10 Maths Formulas for Chapter 3 Pair of Linear Equations in Two Variables Discriminant of a Quadratic Equation The discriminant determines the type of roots and is defined as: D = b² − 4ac It provides immediate insight into the nature before solving the equation fully. Nature of Roots Based on Discriminant For the equation ax² + bx + c = 0: Quadratic Equation from Given Roots If the sum and product of roots are known, form the equation as: x² − (sum of roots)x + (product of roots) = 0 Sum and Product of Roots For the equation ax² + bx + c = 0: Read more: Coordinate Geometry Class 10 Formulas with Solved Examples Applications of Quadratic Equations Class 10 Quadratic equations model situations where values follow a curved or changing pattern. Tips to Learn Quadratic Equations Class 10 Example Example 1: Find the discriminant of the quadratic equationx² − 4x + 5 = 0 and state the nature of its roots. Solution: The given equation follows the form ax² + bx + c = 0, wherea = 1, b = −4, and c = 5. The discriminant isD = b² − 4acD = (−4)² − 4(1)(5)D = 16 − 20D = −4 < 0 Since the discriminant is less than 0, the quadratic equation has no real roots.

Many maths problems do not work with one condition alone. They require two conditions to arrive at a correct answer. This idea forms the base of a pair of linear equations. When two equations represent the same situation, their common solution gives the result. When they fail to meet, no valid answer exists. When they overlap, more than one solution appears. Students apply this concept in questions that compare money, speed, distance, and quantity. The chapter helps you understand how equations behave, how graphs show solutions, and how algebraic methods give exact values. Through Class 10 online CBSE maths tuition, students can strengthen their approach to board questions, focusing on method selection, formula application, and consistency conditions. In this blog, you will learn CBSE Class 10 Maths Chapter 3, Pair of Linear Equations in Two Variables. Along with important formulas, you will read all the required definitions and conditions. Key Definitions and Concepts: Pair of Linear Equations in Two Variables 1. Linear Equation in Two Variables A linear equation in two variables can be written in the formax + by + c = 0,where a, b, and c are real numbers and a and b cannot both be zero.The variables x and y represent unknown values. Read more: Complete Guide to Class 10 Maths Formulas Chapter by Chapter 2. Solution of a Pair of Linear Equations A solution refers to the values of x and y that satisfy both equations at the same time. Only the common values that make each equation true form the solution of the system. 3. Consistent System of Linear Equations A system of linear equations is called consistent when it has at least one solution. The equations may have one solution or infinitely many solutions. Read more: CBSE Class 10 Maths Chapter 2 Polynomials Formula 4. Inconsistent System of Linear Equations A system is inconsistent when no pair of values satisfies both equations. In this case, the equations never meet. 5. Graphical Method for Solving a Pair of Linear Equations Consider the pair:a₁x + b₁y + c₁ = 0 a₂x + b₂y + c₂ = 0 Each equation represents a straight line on the Cartesian plane. The nature of their intersection decides the solution. Read more: Quadratic Equations Formulas CBSE Class 10 Maths Conditions and Their Graphical Meaning Coefficient Condition Line Position Nature of Solution a₁/a₂ ≠ b₁/b₂ Lines intersect One unique solution a₁/a₂ = b₁/b₂ = c₁/c₂ Lines overlap Infinitely many solutions a₁/a₂ = b₁/b₂ ≠ c₁/c₂ Lines remain parallel No solution Graph-Based Interpretation 6. Algebraic Methods to Solve a Pair of Linear Equations Students solve equations algebraically using these standard methods: Read more: Coordinate Geometry Class 10 Formulas with Solved Examples Applications of Pair of Linear Equations in Two Variables Students use a pair of linear equations to solve problems where two conditions control two unknown values. Common Applications Tips to Memorize Chapter 3 Formulas and Concepts Tip 1: Remember the Standard Form Always rewrite equations as:ax + by + c = 0This form helps in checking consistency and applying cross multiplication. Tip 2: Use Ratio Logic for Graph Questions Link ratios with line behavior: Tip 3: Method Selection Shortcut Tip 4: Visual Memory Trick Think of three-line cases only: Every graph question fits one case. Example Based on a Pair of Linear Equations Question: The sum of two numbers is 10. Their difference is 2. Find the numbers. Step 1: Form equationsx + y = 10x − y = 2 Step 2: Solve using eliminationAdd both equations: 2x = 12, x = 6 Step 3: Find yy = 10 − 6y = 4 Answer: The two numbers are 6 and 4.

Polynomials form one of the most essential topics in CBSE Class 10 mathematics. They provide the foundation for understanding equations, algebraic expressions, and the relationship between zeroes and coefficients. A clear grasp of polynomial formulas not only helps in solving academic problems efficiently but also builds a strong base for higher mathematics. In this guide, we cover all major formulas for linear, quadratic, and cubic polynomials, their practical applications, tips to memorize them effectively, and step-by-step examples to help students prepare confidently for their CBSE exams. Understanding Polynomials and Their Types Polynomials are algebraic expressions that involve variables raised to whole-number powers. Depending on their degree: Key Concept: The degree of a polynomial determines the maximum number of roots it can have. Linear polynomials have 1 root, quadratic polynomials have 2, and cubic polynomials have 3. Essential Polynomial Formulas – Class 10 Quadratic Polynomial For a quadratic polynomial ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0, with roots α\alphaα and β\betaβ: Cubic Polynomials For a cubic polynomial ax3+bx2+cx+d=0ax^3 + bx^2 + cx + d = 0ax3+bx2+cx+d=0, with roots α,β,γ\alpha, \beta, \gammaα,β,γ: Additional Formulas Applications of Polynomial Formulas Polynomial formulas are not limited to classroom problems. They are widely applied in various fields: Tips to Memorize Polynomials Formulas Examples of Polynomial Formulas in Action Example 1: Construct a Quadratic Polynomial Problem: Form a quadratic equation whose roots are 4 and -3. Solution: Answer: x2−x−12=0x^2 – x – 12 = 0x2−x−12=0 Example 2: Construct a Cubic Polynomial Problem: Find a cubic polynomial with roots 1, 2, -3. Solution: Answer: x3−7x+6=0x^3 – 7x + 6 = 0x3−7x+6=0 Example 3: Find Roots Using Sum & Product Problem: A quadratic polynomial has sum of roots = 5, product of roots = 6. Form the polynomial. Solution: x2−(sum of roots)x+(product of roots)=x2−5x+6x^2 – (\text{sum of roots})x + (\text{product of roots}) = x^2 – 5x + 6×2−(sum of roots)x+(product of roots)=x2−5x+6 Answer: x2−5x+6=0x^2 – 5x + 6 = 0x2−5x+6=0