Primary 6 Circle Study Guide

Primary 6 circle in six short steps, from rolling out the rim to comparing two shaded regions. Every step has a circle figure to tap through, then come worked examples.

Start here

What are the circumference and area of a circle?

The circumference is the edge rolled out flat; the area is the space inside.

Roll the rim of a circle out into a straight line and measure it in diameters. It is 3 diameters and a little more, every time. That number is pi, written π, so circumference = π × d. Cut the circle into thin pieces and lay them flat, and they make a rectangle: area = π × r × r.

In this chapter, your child learns to:

find a circumference from a radius or a diameter;
find the area of a circle, halving a diameter first;
find the perimeter and area of semicircles and quarter circles;
work on figures joined from rectangles, squares and parts of circles;
read a radius from a shape that fits exactly, and compare two shaded regions.

The rim, rolled out flat, is as long as the edge was.

It is 3 diameters and a bit more. That number is π.

circumference = π × d

area = π × r × r, from Step 2

Step 1

How to find the circumference of a circle

A circumference is pi times the diameter. Write the rule first: circumference = π × d. The rule needs the diameter. When the question gives the radius, the diameter is the radius and the radius again, so double it on its own line first. Then use the value of π the question gives: 3.14 or 22/7.

A circle has a radius of 5 cm. Find its circumference. (Take π = 3.14.)

Tap Next step

circumference = π × d

The circumference is the edge, all the way round. The rule is written first, with no numbers yet. Tap Next step to roll the edge out.

Try it

A round pond has a diameter of 35 m. Find its circumference. (Take π = 22/7.)

Rolling out the circle

Step 2

How to find the area of a circle

Cut the circle up and it lies flat as a rectangle. Slice a circle into thin pieces and lay them in a row, one pointing up, one pointing down. Nothing is lost, so the area is the same. The bottom edge is half the rim, which is π × r, and the height is one radius. Length × breadth gives area = π × r × r. The rule uses the radius twice, so halve a diameter first.

A circle has a radius of 10 cm. Find its area. (Take π = 3.14.)

Tap Next step

area = π × r × r

How do you find the area of something round? Tap Next step to cut it up.

Try it

A round mat has a diameter of 14 cm. Find its area. (Take π = 22/7.)

Cutting the circle up

Step 3

Perimeter of a semicircle and a quarter circle

Go round it: the arc, then every straight edge the cut made. The curved part is called the arc. A semicircle's arc is half of π × d; a quarter circle's is a quarter of it. Cutting a circle makes new straight edges, and they belong to the perimeter: a semicircle has 1, the diameter; a quarter circle has 2, each a radius. Their areas work the same way: half or a quarter of π × r × r.

A semicircle has a radius of 15 cm. Find its perimeter. (Take π = 3.14.)

Tap Next step

Half a circle, radius 15 cm. Perimeter means the whole way round. Tap Next step to go round it.

Try it

A semicircle has a diameter of 14 cm. Find its perimeter. (Take π = 22/7.)

Halves and quarters

Step 4

Perimeter and area of composite figures with circles

Read which one the question wants: how far round, or how much inside. For a perimeter, go round the outside and list every edge. Work out the curves first, on their own line, then add the straight edges in one sum. The edge where two shapes join is inside the figure, so it is not counted. For an area, find each shape's area and add them; when a piece has been cut out, it is the whole minus the piece.

A semicircle is joined to a 20 cm by 14 cm rectangle along a shorter side. (Take π = 22/7.) Find the perimeter of the figure.

Tap Next step

Perimeter is how far round. Tap Next step to go round the outside.

Try it

A quarter circle of radius 7 cm is cut out of the corner of a square of side 7 cm. Find the area of the square that is left. (Take π = 22/7.)

Putting shapes together Adding and subtracting Mixed practice

Step 5

Finding the radius or diameter from a figure

When one shape fits exactly inside another, it is telling you a length. Some figures carry no radius at all. A circle that fits exactly inside a square is as wide as the square, so one side is the diameter. Find that side first, then halve it for the radius. Shapes inside shapes work the same way: where two quarter circles meet at the middle of a side, that side is a whole diameter.

A circle fits exactly inside a square. The perimeter of the square is 56 cm. Find the area of the circle. (Take π = 22/7.)

Tap Next step

area = π × r × r

The rule comes first, every time. But there is no number on the circle. Where does the radius come from?

Try it

A rectangle is 20 cm long and 10 cm wide. Two identical circles fit exactly inside it, side by side. What is the radius of each circle?

Finding the length Shapes inside shapes

Step 6

Finding the difference between two shaded regions

Name the shared piece, and it drops out of the difference. Some questions ask for the difference between two regions, X and Y, that cannot be measured on their own. Name the piece inside both shapes S. X is one whole shape minus S, and Y is the other minus the same S. So X − Y is the difference of the two whole shapes, and S never has to be found.

Square ABCD has sides of 20 cm. A circle of radius 10 cm has its centre at B. X is the part of the square outside the circle; Y is the part of the circle outside the square. Find X − Y. (Take π = 3.14.)

Tap Next step

X and Y have curved edges, and neither can be measured on its own. Write the two regions before any number.

Try it

Square PQRS has sides of 22 cm. A circle of radius 11 cm has its centre at Q. X is the part of the square outside the circle and Y is the part of the circle outside the square. Find X − Y. (Take π = 3.14.)

The difference of two regions

Primary 6 circle questions, worked step by stepWrite the rule first and try each one. Then open a hint, or show the working a line at a time.

CircumferenceBasic

A bicycle wheel has a radius of 35 cm. How far does the wheel move forward in one complete turn? (Take π = 22/7.)

One turn rolls the rim out once along the ground. The rule needs the diameter.

circumference = π × d
Diameter = 2 × 35 = 70 cm.
Circumference = 22/7 × 70 = 22 × 10 = 220 cm.

Answer: 220 cm

Adding and subtractingBasic

A circle of diameter 30 cm is cut out of a square piece of card of side 30 cm. Find the area of card that is left. (Take π = 3.14.)

The card left is the whole square minus the circle. Halve the diameter first.

Square area = 30 × 30 = 900 cm².
Radius = 30 ÷ 2 = 15 cm.
Circle area = 3.14 × 15 × 15 = 706.5 cm².
Card left = 900 − 706.5 = 193.5 cm².

Answer: 193.5 cm²

Putting shapes togetherIntermediate

A running track is made of two straight sides, each 100 m long, and two semicircular ends. Each end has a diameter of 63 m. Find the length of one lap. (Take π = 22/7.)

Curves first. Two equal semicircles make one whole circle.

circumference = π × d
2 semicircular ends = 1 circle = 22/7 × 63 = 198 m.
One lap = 198 + 100 + 100 = 398 m.

Answer: 398 m

Finding the lengthIntermediate

The circumference of a circular table top is 88 cm. Find the area of the table top. (Take π = 22/7.)

Use the circumference to find the diameter, then halve it for the radius.

circumference = π × d, so d = 88 ÷ 22/7 = 88 × 7/22 = 28 cm.
Radius = 28 ÷ 2 = 14 cm.
area = π × r × r = 22/7 × 14 × 14 = 616 cm².

Answer: 616 cm²

Shapes inside shapesChallenge

Square ABCD has sides of 28 cm. A quarter circle of radius 14 cm is drawn at each of its four corners. The part of the square outside the quarter circles is shaded. Find (a) the area and (b) the perimeter of the shaded part. (Take π = 22/7.)

Where do two quarter circles meet on a side? How many quarters make a whole circle?

14 + 14 = 28, so adjacent quarter circles meet at each side's midpoint.
4 quarter circles make 1 circle of radius 14 cm.
Square area = 28 × 28 = 784 cm².
Total quarter-circle area = 22/7 × 14 × 14 = 616 cm².
Shaded area = 784 − 616 = 168 cm².
Circle diameter = 2 × 14 = 28 cm.
Shaded perimeter = 22/7 × 28 = 88 cm.

Answer: (a) 168 cm²; (b) 88 cm

Step 7

Check yourself

Five quick circle questions. Answers are not stored, and each reply points to the type of question it matches.

1. A circle has a diameter of 21 cm. Find its circumference. (Take π = 22/7.)

2. A circle has a radius of 3 cm. Find its area. (Take π = 3.14.)

3. A quarter circle has a radius of 35 cm. Find its perimeter. (Take π = 22/7.)

4. A semicircle of diameter 22 cm is joined to one side of a square of side 22 cm. Find the area of the figure. (Take π = 3.14.)

5. A circle fits exactly inside a square with a perimeter of 40 cm. Find the circumference of the circle. (Take π = 3.14.)

0/5

Answer all five to see where to practise next.

For parents

How to use this guide. Before each Next step, ask your child which rule comes first and whether the radius or the diameter is needed. Then let the figure show it. One step takes a few minutes.

In any circle question, ask your child to say aloud whether it asks how far round or how much inside, and to write the rule on the first line before a single number. A derived radius or diameter goes on its own line, so the number in the rule can be traced back.

More study guides

Before this: Average Next: Volume Primary 4 Area and Perimeter study guide Primary 3 Area and Perimeter study guide Primary 6 Area study guide

Lessons and practice

P6 Circle lessons and practice

9 lesson videos and 102 questions across eight subtopics, from Basic to Challenge, each with a worked solution.

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