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. Understanding these formulas helps solve problems involving tangents, arcs, and combined figures efficiently.

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

Practical Applications of Circle Area Formulas

• Sports and Field Design: Cricket pitches, football fields, and athletics tracks often involve circular sections. Using formulas for circumference, sector, and segment helps calculate boundary lengths, areas for turf, or marked zones accurately.
• Gardening and Landscaping: Circular gardens, fountains, and flower beds require precise measurement for planting or installation. Formulas for area and circumference determine the quantity of soil, grass, or decorative material needed.
• Construction and Architecture: Circular windows, domes, arches, and floor patterns rely on accurate sector and segment calculations to plan dimensions and materials. Architects use these formulas to avoid errors in layout and cost estimation.
• Engineering and Manufacturing: Gears, rings, circular plates, and wheels involve concentric circles. Ring area formulas help calculate material requirements and structural integrity.
• Everyday Measurement Problems: Calculating areas for pizza slices, cake pieces, or circular mats. Estimating paint required for walls with circular designs or clocks.
• Mathematical Problem Solving: CBSE questions often combine sectors, segments, and concentric circles. These formulas enable students to solve multi-step geometry problems efficiently, with precision in length, area, and angle calculations.

Tips to Master Areas Related to Circle Formulas

• Understand, Don’t Memorize: Visualize the shape while learning each formula. Draw the circle, radius, sector, or segment to see how the formula arises.
• Relate Formulas to Real Shapes: Connect the area of a sector with the slice of pizza, the segment with a curved window, and the ring area with circular tracks. Real-world connections improve retention.
• Practice Stepwise Solving: Break problems into smaller steps: identify the radius, angle, or chord first; then apply the correct formula. This reduces mistakes.
• Use Flashcards and Notes: Write formulas on cards or mobile notes for daily quick revision. Include small diagrams for visual memory.
• Compare Related Formulas: Relate the segment area to sector area and triangle inside it. Compare semicircle, quadrant, and full circle formulas to spot patterns.
• Solve Diverse Examples: Include both numerical and word problems. Practice problems with different units like meters, centimeters, and angles in degrees to ensure flexibility.
• Check Units and Accuracy: Always match area units (m², cm²) and length units (m, cm) in multi-step problems. Accuracy matters in exams.

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