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Circle graphs

Each part of 360°, draw the slices; back from an angle · Foundations · 20 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Find the total
  2. Each part of 360°
  3. Draw the circle graph
  4. Check

The steps for Circle graph: cats 12, dogs 18, fish 6, birds 4. Every solution names its steps, so you always know what comes next.

Worked examples

Circle graph: sports 40%, music 35%, art 25% Easy

The question

Question: make a circle graph of sports 40%, music 35%, art 25%.

sports 40%, music 35%, art 25%

A circle graph shows the parts of a whole as slices.

The whole circle is 360 degrees.

the whole circle = 360°

1 Each part of 360°

Sports is 40% of the circle.

40% is 0.4.

0.4 times 360 is 144°.

= sports: 40% × 360 = 0.4 × 360 = 144°

Careful!

A percent is out of 100.

Degrees are out of 360.

40% of the circle is 144°.

Careful: not 40% → 40° ✗

Music: 35% of 360 is 126°.

= music: 35% × 360 = 0.35 × 360 = 126°

Art: 25% of 360 is 90°.

= art: 25% × 360 = 0.25 × 360 = 90°

2 Draw the circle graph

We draw a circle and start at the top.

Sports: a slice of 144°, going round like a clock.

Then music, 126°, and so on.

So the slices are sports 144°, music 126° and art 90°.

= sports 144°, music 126°, art 90°

3 Check

Let's check: the slices fill the circle: 144 plus 126 plus 90 is 360.

So the answer is right!

144 + 126 + 90 = 360

Let's look back.

First: each part of 360°.

Then: draw the circle graph.

Last: check.

Answer
= sports 144°, music 126°, art 90°

▶ Watch it solved

Circle graph: cats 12, dogs 18, fish 6, birds 4 Medium

The question

Question: make a circle graph of cats 12, dogs 18, fish 6, birds 4.

cats 12, dogs 18, fish 6, birds 4

A circle graph shows the parts of a whole as slices.

The whole circle is 360 degrees.

the whole circle = 360°

1 Find the total

First the whole: 12 plus 18 plus 6 plus 4 is 40.

= total = 12 + 18 + 6 + 4 = 40

2 Each part of 360°

Cats: 12 out of 40, that is 3/10.

Of 360 degrees: 108°.

= cats: 1240 = 310 × 360 = 108°

Dogs: 18 out of 40, of 360, is 162°.

= dogs: 1840 = 920 × 360 = 162°

Fish: 6 out of 40, of 360, is 54°.

= fish: 640 = 320 × 360 = 54°

Birds: 4 out of 40, of 360, is 36°.

= birds: 440 = 110 × 360 = 36°

Careful!

The parts are counts, not percents.

Each one is out of the total, 40.

Careful: use the total, not 100

3 Draw the circle graph

We draw a circle and start at the top.

Cats: a slice of 108°, going round like a clock.

Then dogs, 162°, and so on.

So the slices are cats 108°, dogs 162°, fish 54° and birds 36°.

= cats 108°, dogs 162°, fish 54°, birds 36°

4 Check

Let's check: the slices fill the circle: 108 plus 162 plus 54 plus 36 is 360.

So the answer is right!

108 + 162 + 54 + 36 = 360

Let's look back.

First: find the total.

Then: each part of 360°.

Then: draw the circle graph.

Last: check.

Answer
= cats 108°, dogs 162°, fish 54°, birds 36°

▶ Watch it solved

Circle graph: math 8, art 5, music 7, sport 4 Harder

The question

Question: make a circle graph of math 8, art 5, music 7, sport 4.

math 8, art 5, music 7, sport 4

A circle graph shows the parts of a whole as slices.

The whole circle is 360 degrees.

the whole circle = 360°

1 Find the total

First the whole: 8 plus 5 plus 7 plus 4 is 24.

= total = 8 + 5 + 7 + 4 = 24

2 Each part of 360°

Math: 8 out of 24, that is 1/3.

Of 360 degrees: 120°.

= math: 824 = 13 × 360 = 120°

Art: 5 out of 24, of 360, is 75°.

= art: 524 × 360 = 75°

Music: 7 out of 24, of 360, is 105°.

= music: 724 × 360 = 105°

Sport: 4 out of 24, of 360, is 60°.

= sport: 424 = 16 × 360 = 60°

Careful!

The parts are counts, not percents.

Each one is out of the total, 24.

Careful: use the total, not 100

3 Draw the circle graph

We draw a circle and start at the top.

Math: a slice of 120°, going round like a clock.

Then art, 75°, and so on.

So the slices are math 120°, art 75°, music 105° and sport 60°.

= math 120°, art 75°, music 105°, sport 60°

4 Check

Let's check: the slices fill the circle: 120 plus 75 plus 105 plus 60 is 360.

So the answer is right!

120 + 75 + 105 + 60 = 360

Let's look back.

First: find the total.

Then: each part of 360°.

Then: draw the circle graph.

Last: check.

Answer
= math 120°, art 75°, music 105°, sport 60°

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. circle graph: sports 40%, music 35%, art 25%
    Answer
    = sports 144°, music 126°, art 90°
  2. circle graph: walk 50%, bus 25%, car 25%
    Answer
    = walk 180°, bus 90°, car 90°
  3. circle graph: red 30%, blue 45%, green 25%
    Answer
    = red 108°, blue 162°, green 90°
  4. circle graph: yes 60%, no 40%
    Answer
    = yes 216°, no 144°
  5. a circle graph has a 90° slice for walk, what percent walk
    Answer
    = 14 × 100% = 25%
  6. a circle graph has a 180° slice for pizza, what percent pizza
    Answer
    = 12 × 100% = 50%
  7. circle graph: apples 20%, pears 30%, plums 50%
    Answer
    = apples 72°, pears 108°, plums 180°

Medium

  1. circle graph: cats 12, dogs 18, fish 6, birds 4
    Answer
    = cats 108°, dogs 162°, fish 54°, birds 36°
  2. circle graph: soccer 9, tennis 6, swim 15
    Answer
    = soccer 108°, tennis 72°, swim 180°
  3. circle graph: rock 10, pop 25, jazz 5
    Answer
    = rock 90°, pop 225°, jazz 45°
  4. a circle graph of 200 students has a 90° slice for walk, how many walk
    Answer
    = 14 × 200 = 50
  5. a circle graph has a 72° slice for bike, what percent bike
    Answer
    = 15 × 100% = 20%
  6. circle graph: rent 35%, food 25%, fun 15%, save 25%
    Answer
    = rent 126°, food 90°, fun 54°, save 90°
  7. a circle graph of 120 people has a 60° slice for tea, how many tea
    Answer
    = 16 × 120 = 20

Harder

  1. circle graph: math 8, art 5, music 7, sport 4
    Answer
    = math 120°, art 75°, music 105°, sport 60°
  2. circle graph: car 45%, bus 20%, bike 10%, walk 25%
    Answer
    = car 162°, bus 72°, bike 36°, walk 90°
  3. a circle graph of 360 voters has a 135° slice for yes, how many yes
    Answer
    = 38 × 360 = 135
  4. a circle graph has a 54° slice for green, what percent green
    Answer
    = 320 × 100% = 15%
  5. circle graph: A 15, B 21, C 9, D 27
    Answer
    = A 75°, B 105°, C 45°, D 135°
  6. a circle graph of 80 kids has a 144° slice for soccer, how many soccer
    Answer
    = 25 × 80 = 32