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 problems also build logical reasoning skills used in coordinate geometry, trigonometry, and mensuration. Many real-world objects, such as wheels, gears, pipes, and orbits, follow circular geometry, which makes this topic both practical and foundational.

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

• Perimeter of a circle
  Perimeter = 2 × π × radius
• Surface area enclosed by a circle
  Area = π × radius × radius

Formulas Related to Sectors and Arcs

• Length of an arc
  Arc length = (central angle ÷ 360) × full circumference
• Area of a sector
  Sector area = (central angle ÷ 360) × area of the circle

Formula for a Segment of a Circle

• Area of a segment
  Segment area = area of sector − area of triangle formed by the radii and chord

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.

• Science and Engineering
  Scientists use circle formulas to design rotating instruments such as centrifuges, turbines, and particle separators. Engineers calculate the circumference and area of circular components to ensure balance and accuracy.
• Astronomy and Space Studies
  Astronomers apply circle formulas to compare the sizes of planets, moons, and satellites. These formulas also help estimate orbital paths and circular trajectories in space models.
• Sports and Athletics
  Sports authorities use circle geometry while designing running tracks, throwing areas, and stadium layouts. Accurate radius and arc length calculations ensure standard measurements.
• Architecture and Construction
  Architects use circle formulas to design domes, arches, fountains, and circular halls. Builders calculate material requirements using area and perimeter values.
• Daily Life Applications
  Circle formulas help measure wheels, pipes, lids, plates, and round containers. These calculations assist in cost estimation and material usage.

Tips to Learn and Remember Circle Formulas for Class 10

Learning circle formulas becomes easier when students focus on understanding instead of memorising.

• Know Every Term Clearly
  Understand the meaning of radius, diameter, chord, arc, sector, and segment before using formulas. Clear concepts reduce calculation mistakes.
• Link Each Formula to Its Use
  Connect circumference with boundary problems and area with surface coverage questions. This method helps identify the correct formula quickly.
• Practice Stepwise Solutions
  Write each step clearly during practice. CBSE marking schemes reward method and substitution accuracy.
• Draw a Diagram First
  A labeled diagram helps identify the radius, angle, and required region. Visual clarity improves formula selection.
• Revise Using Formula Tables
  Use a single formula sheet for daily revision. Rewriting formulas improves memory retention.
• Solve NCERT and Sample Papers
  Focus on textbook problems and board-level questions. These patterns repeat often in exams.

Solved Examples Using Circle Formulas

Example 1

Find the area of one-fourth of a circle when its perimeter measures 42 cm.

• Perimeter = 42 cm
• Radius = 42 ÷ (2 × 3.14)
• Radius = 6.68 cm

Quadrant area = (π × radius²) ÷ 4
Final 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 × 5
Final answer = 4.36 cm