Pie Charts (Math) Free Worksheets & Q/A

Pie Charts

 A convenient way of comparing data is by using pie charts. In pie charts, a circle is divided into parts and then the parts are compared. Since it looks like a pie that has been sliced into pieces, such a diagram is known as a pie chart. 

* Pie graphs are convenient for displaying information of the type that are measures of part of a whole, given as fractions, ratios, or percentages.

* A pie chart is constructed by dividing a circle into different sectors.

For example, the pie chart given alongside shows the different fruits that a fruit seller keeps at his shop. We can see that out of all the fruits in the shop, mangoes are the most in number, followed by pears, apples and then oranges.

The circle represents the total number of fruits surveyed.

The pie chart shows the favourite pastimes of 160 students.

Study the pie chart and answer the following questions.

a) What is the favourite pastime of most number of students?

b) Between indoor and outdoor games, which is more popular?

c) Between outdoor games and reading, which is less popular?

d) How many students chose reading as their favourite pastime?

Ans: 

a) In the pie chart, reading covers the most area. Thus, reading is the favorite pastime of most number of students.

b) In the pie chart, outdoor games covers more area than indoor games. Thus, outdoor games are more popular than indoor games.

c) In the pie chart, outdoor games covers less area than reading. Thus, outdoor games is less popular than reading.

d) In the pie chart, reading covers half of the area. The entire circle represents 160 students. Half of 160 is 160/2 = 80. Thus, 80 students chose reading as their favourite pastime.

 Q. Study the given pie chart and answer the following questions.

a) Which is the most popular hobby among the students? sports
b) Which is the least popular hobby among the students? watching TV
c) Between music and reading, which is more popular? reading
d) Between reading and watching TV, which is more popular? Reading
e) How many different hobbies do the students have in all? 4

Q. The boys of grade 5 of St. Mark's School were asked to pick their favourite sport. their response is represented in the following pie chart.

a) Which is the most popular sport among the boys? Cricket

b) Which is the least popular sport among the boys? Tennis

c) Between tennis and badminton, which sport is more popular among the boys? badminton

d) Between football and cricket, which sport is more popular among the boys? cricket

Q.1.  A survey is conducted to find out which of the four ice-cream flavours, chocolate, yam, mango and vanilla, the students in a class prefer. The pie chart shows the results of the survey.

i) If one-quarter of the class prefers yam, state the angle of the sector that represents this information.
ii) Find the angle of the sector that represents the number of students who prefer vanilla.
iii) If 5 students prefer mango, find the total number of students in the class.
iv) Express the number of students who prefer vanilla as a percentage of the total number of students in the class.

Solution:

 i) If one-quarter of the class prefers yam, state the angle of  

                   the sector that represents  = 90
                                    ii) Sum of angles = 360
Total number of students who prefer chocolate, yam, mango = ( 120 + 90 + 50)
                                                                                                                = 260
The number of students who prefer vanilla = (360 - 260)
                                                                            = 100 Ans.
iii) If 5 students prefer mango, 
so the total number of students in the class = 360/50  X 5
                                                                            = 36 Ans.

Free WorkSheet you can download:

Q.2. The pie chart shows the sources of revenue of a publishing company.
i) Express the revenue the company earns from newspapers as a percentage of the total revenue of the company.

ii) Express the revenue of the company earns from magazines as a percentage of the total revenue of the company.
iii) If the revenue the company earns from books is 17.5 % of the total revenue of the company, find the value of x.

 Solution:

       i) 180/360 X 100%

               = 50% Ans.

     ii) 72/360 X 100%

        = 20% Ans

Q.3. The pie chart shows the nutritional composition of a food product.
i) Calculate the value of x.
ii) Express the amount of fat as a percentage of the components of the food product.
iii) Given that a food product contains 120 g of carbohydrates, 
     calculate the mass of the food product.

Solution: 
i) 144⁰  + 9x⁰  + 2x⁰ + x⁰  = 360⁰ 
                               12x⁰  = 360⁰  -  144⁰ 
                                         = 216⁰
                                    x⁰   = 18⁰
                                        x = 18
ii) Angle of sector representing the amount of fat in the food product 

                                                         = 2 x 18⁰  = 36⁰
                       Required percentage = 36⁰/360⁰  x 100%
                                                            = 10%
iii) The angle of the sector representing carbohydrates is 144⁰ and 

this constitutes 120 g.
Mass of the food product = 360⁰ / 144⁰   x 120
                                            = 300 g

Q.4. The pie chart shows the composition of a jar of fruit punch.

i) Find the value of x.
ii) Express the amount of apple juice in the fruit punch as a percentage of all the components in the fruit punch.
iii) Given that a jar of fruit punch contains 759 ml of cranberry juice, find the amount of fruit punch in the jar.

Solution:

i) 237.6⁰ + 4x⁰ + 2x⁰  = 360⁰

             or, 6x⁰  = 360⁰ - 237.6⁰

               or, x⁰= 20.4 Ans.

ii) Angle of sector representing the amount of apple juice in the fruit punch = 4x⁰ 

                                                                                 = 4 x 20.4

                                                                                   = 81.6

                           Required percentage = 81.6/360  x 100%

                                                              = 22.67% Ans.
iii) The angle of the sector representing cranberry juice is 237.6⁰ 

                           and this contains 759 ml.

Q. 5. The pie chart shows the distribution of students and teachers in a school.

a) If there are five times as many female students as teachers in the school, find the angle of the sector that represents the number of teachers in the school.

b) If there are 45 teachers in the school,

i) find the number of female students in the school,

ii) find the number of male students in the school.

c) If 2/3 of the teachers are women, express the number of females in the school as a percentage of the total school population.

Q.6. The monthly expenditure of Raj is presented in a 3-dimensional pie chart and a 2-dimensional pie chart respectively.

i) Based on hte 3-dimensional pie chart, which item does Raj spend the most on?

ii) Based on the 2-dimensional pie chart, which items does Raj spend the most on?

iii) Suggest a reason to explain the discrepany between your answer in (i) and (ii).

Q.7. The pie chart shows Devi's monthly expenditure.
If the amount she spends on clothes is their times as much as that she spends on food,
i) express the amount she spends on food as a percentage of that she saves, 40%
ii) find her annual income. $48,000

Q.8. The pie chart shows the cost breakdown of a holiday.
a) Find the percentage of the cost that was spent on
i) food        80%
ii) hotel
b) If 15% of the total cost was spent on travel, find the value of x.     20.7

Q. 9. Climate change is defind as significant variations in the statistical observations of the weather conditions, which occur over an extended period of time.

a) An indication of climate change is the overall increase in the annual mean surface temperature. Studies show that the annual mean surface temperature is Singapore has increased from 26.8⁰C in 1948 to 27.6⁰C in 2011. Find the percentage increase in the annual mean surface temperature in Singapore from 1948 to 2011, giving your answer correct to 2 decimal places.

b) One of the contributors of climate change is greenhouse gas emissions. Singapore's emissions were 41 million tonnes (MT) in 2005. Singapore's Business-As-Usual (BAU) emissions are expected to reach 77.2 MT in 2020. The pie chart shows a projection of Singapore's BAU emissions for the year 2020 for various sectors.

Source: National Climate Change Secretariat, Prime Minister's Office (Singapore)

Note: Others include waste, water and other electricity use.

i) Which of the above accounts for the majority of Singapore's projected emissions in 2020? Find the amount of emissions contributed by that sector.

ii) Give two reasons for the likely increase in emissions from 2005 to 2020.

c) Find out some measures that have been put in place by the Singapore government to reduce emissions and to mitigate the effects of climate change.