Problem Set 31 – Circumference and Arcs of a CircleClass 5 Maths · Chapter 7 Circles · Problem Set 31 – Maharashtra Board

Summary: Problem Set 31 – Circumference and Arcs of a Circle

The length of the boundary of a circle is called its circumference.

To measure it, wind a string once round the circular edge, straighten it and measure it with a ruler or a measuring tape.

Any part of a circle is called an arc. Two points on a circle split it into two arcs.

Both arcs have the same two end points, so we name each arc with three letters: an end, a point on that arc, and the other end.

If there are 4 points on a circle, they split it into 4 small arcs, one between each pair of neighbouring points.

Key points to remember

• Circumference = length all round the circle
• Measure it with a string or a measuring tape
• Arc = a part of the circle
• 2 points on a circle → 2 arcs
• Arc names use 3 letters
• The middle letter is a point on that arc
• Arc KLM and arc MLK are the same arc
• n points in a row round a circle → n small arcs

Problem Set 31 – Circumference and Arcs of a Circle – Notes

1. What is circumference?

• Walk once round a circular park. The distance you walk is the circumference of the park.
• The circumference is a length, so it is measured in cm, m and so on.
• Bigger circles have bigger circumferences.

2. Measuring with a string

• Wrap a string once round the edge of a bowl or a bangle so that the ends just meet.
• Mark the place where they meet, unwind the string and pull it straight.
• Measure the straight string with a ruler. That length is the circumference.

3. What is an arc?

• If a round bangle breaks in two places, each broken piece is an arc.
• Mark two points G and H on a circle. They cut the circle into two arcs.
• Both arcs start at G and end at H, so 'arc GH' does not tell us which one we mean.

4. Naming arcs

• Take one more point on the arc you mean and put it in the middle of the name.
• If J is on one arc and K is on the other, the arcs are arc GJH and arc GKH.
• Arc GJH can also be read as arc HJG — it is the same arc.

5. Several points on a circle

• Points A, B, C, D placed in order round a circle cut it into 4 small arcs: arc AB, arc BC, arc CD and arc DA.
• To name a small arc clearly, use a point that lies between its two ends, or name a bigger arc like arc ABC.
• The two arcs between A and C are arc ABC and arc ADC.

Formulas at a glance

Key terms

Problem Set 31 – Circumference and Arcs of a Circle – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 31 – Circumference and Arcs of a Circle – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 31 – Circumference and Arcs of a Circle

⏱ About 25 minutes

1. Learn (5 min)
   Learn the meanings of circumference and arc, and the three-letter name for an arc.
2. Measure (15 min)
   Measure the circumference of a bangle, a plate and a bottle lid with a string or tape. Mark 4 points on a circle and name the arcs.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.