Grade 9 Circumference of a Circle: Short Notes

9 ශ්‍රේණිය · 18 පරිච්ඡේදය · වෘත්තයක පරිධිය

57%

of Grade 9 term tests include it (23 of 40)

202

marks in past papers (34 questions)

9 min

full lesson with quick checks

🎯 What you'll learn

Name the radius, diameter and circumference and relate d = 2r
Explain π as circumference ÷ diameter
Find the circumference from the radius or diameter, and back
Find the arc and perimeter of a semicircle
Solve problems with wheels, tracks and fences

How many turns to school?

Kamal cycles 2.2 km to school in Kurunegala. His bicycle wheel is 70 cm across. Every turn of the wheel carries him forward by exactly one circumference. By the end of this lesson you can work out how many times the wheel turns on the way.

Parts of a circle

• Radius (r): centre to the circle.• Diameter (d): straight across through the centre, d = 2r.• Circumference (C): the distance all the way round.Wrap a string round a tin lid and compare it with the diameter: C is always a little over 3 times d. This number is π, about 22/7 or 3.14.

Radius, diameter, circumference

Red: radius r. Blue: diameter d = 2r. Amber: circumference C, all the way round.

🧮 Circumference

Use πd when you know the diameter and 2πr when you know the radius. Take π = 22/7 unless told otherwise; it works neatly with multiples of 7.

C = πd = 2πr

✏️ A round table top

A round table top has diameter 140 cm. Find the length of edging tape needed to go once round it. (π = 22/7)

1C = πd = 22/7 × 140
2140 ÷ 7 = 20, so C = 22 × 20 = 440 cm

✅ 440 cm (4.4 m)

⚠️ Radius or diameter?

The most common error in this chapter is using the diameter as the radius: putting r = 14 into 2πr when 14 cm is the diameter, and getting 88 cm instead of 44 cm. Underline which one the question gives. If it's the diameter, use πd, or halve it first.

✏️ Working backwards

The circumference of a circular well in a Jaffna garden is 8.8 m. Find its diameter and radius. (π = 22/7)

1πd = 8.8, so d = 8.8 ÷ 22/7 = 8.8 × 7/22
28.8 ÷ 22 = 0.4, so d = 0.4 × 7 = 2.8 m
3r = d ÷ 2 = 1.4 m

✅ d = 2.8 m, r = 1.4 m

Semicircles

A semicircle is half a circle.• Its curved edge (arc) is half the circumference: ½ × 2πr = πr.• Its perimeter also includes the straight diameter: πr + 2r.Read the question: 'length of the arc' or 'perimeter'?

⚠️ Whole circle or half? Arc or perimeter?

Two classic slips with semicircles: using the full circumference (44 m instead of 22 m), and adding the diameter when only the arc was asked (or forgetting it when the perimeter was asked). Sketch the shape and trace its edge with your pencil before you calculate.

📌 Remember

• d = 2r. Check which one you are given.• C = πd = 2πr, with π ≈ 22/7 or 3.14.• To go back: d = C ÷ π.• Semicircle: arc = πr; perimeter = πr + 2r.• One wheel turn = one circumference; posts on a closed loop = number of gaps.

🧾 Quick revision sheet

Circumference formula	C = πd = 2πr
Diameter and radius	d = 2r
What is π?	Circumference ÷ diameter, about 22/7 or 3.14.
Arc of a semicircle	πr
Perimeter of a semicircle	πr + 2r
Circumference when d = 7 cm	22 cm
Diameter from circumference	d = C ÷ π
Distance in one turn of a wheel	One circumference.