Pie Charts

From the pie chart, we can see that the slice representing red jumpers is a right angle which tells us that this slice is exactly one quarter of the circle.

Therefore, one quarter of the class wore a red jumper on this non-uniform day:

$32text{ students}div4 = 8text{ students}$

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We have to work out the size of the angle that each grade ‘slice’ should have. We know that John recorded the grades of 24 pieces of homework $(6+5+10+3=24)$.If $6$ of the $24$ pieces of homework were awarded a grade A, we can write this as a fraction :$dfrac{6}{24}$ or $dfrac{1}{4}$.

Therefore $frac{1}{4}$ of the pie will be the slice for grade A so one quarter of the whole pie chart will be a slice with a right-angle $(90degree)$ since,

$360degree div 4 = 90degree$

Homework that was awarded a grade B can be expressed as the following fraction:$dfrac{5}{24}$. Since we know that there are $360degree$ in a circle, then the angle for the grade B slice must be $frac{5}{24}$ of $360degree$:

$dfrac{5}{24} times 360degree = 75degree$

The angle for the grade C slice must be $frac{10}{24}$ of $360degree$:

$dfrac{10}{24} times 360degree = 150degree$

The angle for the grade D slice must be $frac{3}{24}$ of $360degree$:

$dfrac{3}{24} times 360degree = 45degree$

Drawing the circle with a compass, and measuring the angles with a protractor, we should have a pie chart like the one shown below:

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We know that $510$ cars passed underneath the bridge and that the number of yellow cars is represented by a slice of $60$ degrees.

We know that in a circle there is a total of $360degree$, thus the proportion of yellow cars can be expressed as the following fraction:

$dfrac{60degree}{360degree}$

If $frac{60}{360}$ of the total number of cars were yellow, then the number of yellow cars can be calculated as follows:

$dfrac{60}{360}times 510text{ cars} = 85text{ yellow cars}$

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a) We first need to calculate how many cars are represented by $1degree$.

We know that $600$ Kia cars is $40degree$ so we can work out what $1degree$ is:

$dfrac{600}{40} = 15$

Then if Renault is $85degree$ we can find this from our value for $1degree$.

$85 times 15 = 1275$

So there were $1275$ Renault cars in the car park.

b) Similarly to part a, we can find the total by multiplying our value for $1degree$ by $360$ instead of $85$.

$text{ Total Cars} = 15 times 360 = 5400$

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The first thing we need to work out in this question is the amount of time that Oliver spends playing golf.

We are told that he has $12$ hours of leisure time in total and that this is represented by a $60degree$ slice of the pie chart.  Since we know that there are $360degree$ in a circle, then the proportion of the time that Oliver spends playing golf can be expressed as follows:

$dfrac{60degree}{360degree}$

We can therefore calculate the amount of time he playing golf as follows:

$dfrac{60}{360}times12text{ hours} = 2 text{ hours}$

If Lewis spends $2$ hours of the available $9$ playing golf, this will be represented by $frac{2}{9}$ of the pie chart. Since the pie chart is a full circle $(360degree)$, then the slice of the pie chart can be calculated as follows:

$dfrac{2}{9} times 360degree = 80degree$

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