NCERT Mathematics, Class 10, textbook pages 154–160

How to help your child with Class 10 Maths Chapter 11, Areas Related to Circles, at home

Areas of sectors and segments, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

θsector = (θ/360) × πr²

NCERT Class 10 Maths Chapter 11 Areas Related to Circles: what it teaches

Your teen finds areas and arc lengths of sectors using the fraction θ/360 of a circle, and areas of segments (sector minus triangle), with practical problems like wipers and designs.

Why it matters later. Sector areas are used in surface area, radians (Class 11) and design.

See it: this chapter in pictures

r = 7, θ = 90°area = ¼ × 154= 38.5 cm²
A quarter circle.
arc = (θ/360) × 2πr= ¼ × 44= 11 cm
Same fraction of the circumference.
segment = sector − triangle60° segment, r = 6= 6π − 9√3 ≈ 3.26
Subtract the triangle.

You need

  • compass and protractor
  • a pizza or roti
  • a calculator

Tonight’s 45 minutes

  1. Area of a sector of radius 7 cm, angle 90° (38.5 cm²).
  2. Arc length of the same sector (11 cm).
  3. Area swept by a wiper of length 25 cm through 115°.
  4. Area of a segment: sector minus triangle.

Words to use

  • sector
  • segment
  • arc
  • θ/360
  • radius

Watch for

  • Using diameter in πr². Use radius.
  • Forgetting θ/360. A sector is a fraction of the whole circle.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You90° sector, r = 7?

Your child¼ × 154 = 38.5 cm².

A game for this week: Pizza maths

  1. Cut a pizza or roti into sectors.
  2. Measure angles.
  3. Calculate each area.
  4. Check the total equals πr².

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Pizza slices.
  • Clock hand sweeps.
  • Car wipers.
  • Garden sprinklers.

Quick check

Ask these at the end of the week. Tap to see the answer.

Area of 90° sector, r = 7 (π = 22/7)?

38.5 cm².

Arc length of that sector?

11 cm.

Fraction of the circle for 60°?

1/6.

Ready for the next chapter when your child…

  • Finds sector areas and arc lengths.
  • Finds segment areas.
  • Solves design problems.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

How do I find a sector’s area?

(θ/360) × πr².

What is a segment?

The region between a chord and the arc.

Which π value should I use?

As the question says: 22/7 or 3.14.