## 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  =  45o, B  =   60o, C  =  75o, D  =  60o, E  =  120o

Area of sector  =  (θ/360) x πr2

b)  Store A :

=  (45/360) x 72

=  9 million

 Store B :=  (60/360) x 72=  12 million Store C :=  (75/360) x 72=  15 million Store D :=  (60/360) x 72=  12 million Store E :=  (120/360) x 72=  24 million

Problem 3 :

On a pie chart a sector has an angle of 30o 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 72o ?

Solution :

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

(θ/360) x πr=  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  =  15o, O  =  160o, A  =  125o, B  =  60o

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

πr=  7/0.0416

=  168 people

Number of people surveyed is 168 people.

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