Drawing Pie Charts

$360 \div 40 = 9$, so each student is $9^\circ$.

Check: $126^\circ + 90^\circ + 81^\circ + 45^\circ + 18^\circ = 360^\circ$.

$360 \div 120 = 3$, so each item is $3^\circ$.

Water bottles: $46 \times 3^\circ = 138^\circ$

Umbrellas: $34 \times 3^\circ = 102^\circ$

Stationery: $28 \times 3^\circ = 84^\circ$

Jackets: $12 \times 3^\circ = 36^\circ$

Check: $138^\circ + 102^\circ + 84^\circ + 36^\circ = 360^\circ$.

The percentages make up the whole, $100\%$: Others $= 100\% - 30\% - 25\% - 20\% - 15\% = 10\%$.

Each $1\%$ is $3.6^\circ$.

Chicken rice: $\frac{30}{100} \times 360^\circ = 108^\circ$

Nasi lemak: $\frac{25}{100} \times 360^\circ = 90^\circ$

Laksa: $\frac{20}{100} \times 360^\circ = 72^\circ$

Roti prata: $\frac{15}{100} \times 360^\circ = 54^\circ$

Others: $\frac{10}{100} \times 360^\circ = 36^\circ$

Check: $108^\circ + 90^\circ + 72^\circ + 54^\circ + 36^\circ = 360^\circ$.

Other things: $300 - 125 - 40 - 75 = 60$, so she spends $60 on other things.

Food: $\frac{125}{300} \times 360^\circ = 150^\circ$

Transport: $\frac{40}{300} \times 360^\circ = 48^\circ$

Savings: $\frac{75}{300} \times 360^\circ = 90^\circ$

Other things: $\frac{60}{300} \times 360^\circ = 72^\circ$

Check: $150^\circ + 48^\circ + 90^\circ + 72^\circ = 360^\circ$.

Draw a circle, mark its centre and draw a radius straight up. With the protractor's base line along that radius, measure $150^\circ$ for Food and draw the radius. Turning the protractor about the centre each time, measure $48^\circ$ for Transport from that radius, then from the next one $90^\circ$ for Savings. The part left is Other things: measure it to check that it is $72^\circ$. Label each sector and add a title.

$360 \div 26$ is not a whole number, so use each fraction and round at the end.

Fried chicken: $\frac{11}{26} \times 360^\circ \approx 152.31^\circ$, which is $152^\circ$ to the nearest degree

Pizza: $\frac{8}{26} \times 360^\circ \approx 110.77^\circ$, which is $111^\circ$

Curry puffs: $\frac{4}{26} \times 360^\circ \approx 55.38^\circ$, which is $55^\circ$

Popiah: $\frac{3}{26} \times 360^\circ \approx 41.54^\circ$, which is $42^\circ$

Check: $152^\circ + 111^\circ + 55^\circ + 42^\circ = 360^\circ$, so no change is needed.

The rounded angles add up to $142^\circ + 85^\circ + 66^\circ + 38^\circ + 28^\circ = 359^\circ$. The working is right, so the missing $1^\circ$ comes from rounding.

The sum is too small, so add $1^\circ$ to the angle that was rounded down the most. Watermelon went down by $0.11^\circ$, Apple by $0.26^\circ$, Papaya by $0.32^\circ$ and Honeydew by $0.42^\circ$ (Pineapple was rounded up). Honeydew went down the most, so it becomes $29^\circ$.

Check: $142^\circ + 85^\circ + 66^\circ + 38^\circ + 29^\circ = 360^\circ$.

The total number of parts is $4 + 5 + 2 + 1 = 12$.

One part is $360^\circ \div 12 = 30^\circ$.

Food: $4 \times 30^\circ = 120^\circ$

Games: $5 \times 30^\circ = 150^\circ$

Decorations: $2 \times 30^\circ = 60^\circ$

Prizes: $1 \times 30^\circ = 30^\circ$

Check: $120^\circ + 150^\circ + 60^\circ + 30^\circ = 360^\circ$.

The total of $4200 is not needed for the angles: the ratio alone fixes what fraction of the whole each part is. (Working through the amounts gives the same angles: food is $\frac{4}{12}$ of $4200, which is $1400, and $\frac{1400}{4200} \times 360^\circ = 120^\circ$.)

Pop: $\frac{18}{45} \times 360^\circ = 144^\circ$, not $162^\circ$. Wei Jie's $162^\circ$ is $\frac{18}{40} \times 360^\circ$: he divided by 40 instead of the total, 45. Every one of his angles is $9^\circ$ for each student, as for 40 students.

For 45 students, each student is $360^\circ \div 45 = 8^\circ$.

Pop: $18 \times 8^\circ = 144^\circ$

K-pop: $12 \times 8^\circ = 96^\circ$

Rock: $9 \times 8^\circ = 72^\circ$

Classical: $6 \times 8^\circ = 48^\circ$

Check: $144^\circ + 96^\circ + 72^\circ + 48^\circ = 360^\circ$.

$360 \div 120 = 3$, so each item is $3^\circ$.

Exercise books: $64 \times 3^\circ = 192^\circ$

Pens: $26 \times 3^\circ = 78^\circ$

Files: $18 \times 3^\circ = 54^\circ$

Erasers: $12 \times 3^\circ = 36^\circ$

Check: $192^\circ + 78^\circ + 54^\circ + 36^\circ = 360^\circ$.

The Exercise books sector, $192^\circ$, is more than $180^\circ$ and cannot be measured in one go with a protractor. So draw Pens ($78^\circ$), Files ($54^\circ$) and Erasers ($36^\circ$) first, each from the line before. The part left is Exercise books: check it by calculation, $360^\circ - 78^\circ - 54^\circ - 36^\circ = 192^\circ$.

(a) Each Secondary 1 student is in exactly one class, so the four classes make up the whole 160. A pie chart can show it.

(b) Seven temperatures are not parts of one whole; adding them up means nothing. A pie chart cannot show them. A line graph shows how the temperature changes from day to day.

(c) A student can say "yes" to more than one question, so the three counts can add up to more than 30. They are not parts of one whole, so a pie chart cannot show them. A bar graph can.

Netball and volleyball together: $40 - 14 - 6 = 20$ students.

Netball is 3 parts and volleyball 1 part, 4 parts in all: one part is $20 \div 4 = 5$, so 5 chose volleyball and $3 \times 5 = 15$ chose netball.

$360 \div 40 = 9$, so each student is $9^\circ$.

Check: $126^\circ + 135^\circ + 45^\circ + 54^\circ = 360^\circ$.

Check the whole: $32.5\% + 27.5\% + 18.5\% + 12.5\% + 9\% = 100\%$.

Lawns: $\frac{32.5}{100} \times 360^\circ = 32.5 \times 3.6^\circ = 117^\circ$

Woodland: $27.5 \times 3.6^\circ = 99^\circ$

Playgrounds: $18.5 \times 3.6^\circ = 66.6^\circ$, which is $67^\circ$ to the nearest degree

Ponds: $12.5 \times 3.6^\circ = 45^\circ$

Paths: $9 \times 3.6^\circ = 32.4^\circ$, which is $32^\circ$ to the nearest degree

Check: $117^\circ + 99^\circ + 67^\circ + 45^\circ + 32^\circ = 360^\circ$, so no change is needed.