PROBLEMS ON PIE CHART WITH SOLUTIONS

Problem 1 :

A survey of eye color in a class of 30 teenagers revealed the following results

a) Illustrate these results on a pie chart.

b) What percentage of the group have:

i) green eyes ii) blue or grey eyes?

Solution :

(a)

(b) 

(i)  Percentage of people who have green eyes  =  6  2/3%

(ii)  Percentage of people who have blue or gray eyes

=  (23  1/3 + 30)%

=  53  1/3%

Problem 2 :

A business has a major store in five cities. We will call the stores A, B, C, D and E. The pie chart shows the proportion of sales for each store.

a) Use your protractor to measure the size of each sector angle.

b) If the total sales from all stores is $72 million, find the sales made by each of the stores.

Solution :

a) A  =  45^o, B  =   60^o, C  =  75^o, D  =  60^o, E  =  120^o

Area of sector  =  (θ/360) x πr²

b)  Store A :

=  (45/360) x 72

=  9 million

Problem 3 :

On a pie chart a sector has an angle of 30^o and this represents 171 people.

a) How many people are represented by the whole chart?

b) How many people would be represented by a sector of size 72^o ?

Solution :

(a)  Area of sector with an angle 30^o and it represents 171 people.

(θ/360) x πr²  =  171

(30/360) x πr²  =  171

πr²  =  171/0.0833

πr²  =  2052 people

So, the whole chart represents 2052 people.

(b)  Area of sector with angle measure 72 

=  (72/360) x 2052

=  410 people

Problem 4 :

A random sample of people are surveyed about their blood type. The results are displayed in the pie chart opposite.

a) Use your protractor to measure the size of each sector angle.

b) What percentage of people surveyed have type A blood?

c) If 7 of the people surveyed have type AB blood, how many people were surveyed in total?

Solution :

a) AB  =  15^o, O  =  160^o, A  =  125^o, B  =  60^o

b)  Percentage of of people surveyed for type A :

=  (125/360) x 100%

=  34.7%

c)  Number of people surveyed have type AB  =  7

(15/360) x πr²  =  7

πr²  =  7/0.0416

=  168 people

Number of people surveyed is 168 people.

Problem 5 :

A pie chart below shows what games consoles the students at Helanbacagun Primary School in North Wales received for Christmas.

If 6 lucky students got a ZX81, how many students got an XBOX one ?

Solution :

Number of students got ZX81 = 6

(θ/360) x πr² = 6

(30/360) x πr² = 6

πr² = 6 x (360/30)

πr² = 6 x 12

πr² = 72

Area of circle is 72 square units.

Number of students got XBOX one = (θ/360) x πr²

= (100/360) x 72

= 10 x 2

= 20 students.

Problem 6 :

A pie chart shows how a group of children travel to school.

195 children go to school by bike. How many children take the bus to school ?

a)  325   b)  420     c)  315     d)  400

Solution :

Number of children go to school by bike = 195

(θ/360) x πr² = 195

Here θ = 65

(65/360) x πr² = 195

πr² = 195 x (360/65)

πr² = 1080

Number of children go to school by bus

= (θ/360) x πr²

= (140/360) x 1080

= 420

So, the number of children go by bus is 420.

Problem 7 :

A bag contains red, white and black counters. The pie chart below shows information about the counters in the bag.

There are 48 counters in the bag. How many counters are black ?

Solution :

Angle measure at black = 360 - (90 + 120)

= 360 - 210

= 150

Total number of counters = 48

Number of counters in black = (θ/360) x πr²

= (150/360) x 48

= 20

So, total number of counters in black is 20.

Problem 8 :

A class of 36 pupils were asked to pick their favorite color from green, purple or red.

(i) The whole year group were asked the same question. The pie chart looked exactly the same. If 30 pupils chose purple how many pupils are in the year group ?

Solution :

Total number of pupils = 36

Number of people who chose purple = 30

Angle measure for purple = 180 - 30

= 150

Area of sector = (θ/360) x πr²

(150/360) x πr² = 30

 πr² = 30 x (360/150)

 πr² = 72

The entire circle will represents 72, then the total number of pupils in the group is 72.

Problem 9 :

A class of 36 pupils were asked to pick their favorite color from green, purple or red.

(i) What is the probability that a pupil chosen at random chose purple or green ?

(ii) What is the probability that a pupil chosen at random chose red or green ?

Solution :

(i)

Total number of pupils = 36

Number of pupil who choose green = (30/360) x 36

= 3

Number of pupil who choose purple = (θ/360) x πr²

= (150/360) x 36

= 15

Number of pupil who choose purple or green = 15 + 3

= 18

Probability of choosing purple or green = 18/36

= 1/2

(ii)  Number of pupil who choose red = 36 - 18

= 18

Number of pupil who choose red or green = 18 + 3

= 21

Probability of choosing pupil who choose red or green 

= 21/36

= 7/12

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