Pie Charts: Practice Problems Grade 7
A pie chart (also called a Pie Graph or Circle Graph) makes use of sectors in a
circle. The angle of a sector is proportional to the frequency of the data.
The formula to determine the angle of a sector is:
𝑨𝒏𝒈𝒍𝒆 𝒐𝒇 𝒔𝒆𝒄𝒕𝒐𝒓 =
𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒔𝒆𝒄𝒕𝒐𝒓
× 𝟑𝟔𝟎𝒐
𝒕𝒐𝒕𝒂𝒍 𝒗𝒂𝒍𝒖𝒆
Study the following steps of constructing a circle graph:
Step 1 : Calculate the angle of each sector, using the formula
Step 2 : Draw a circle using a pair of compasses
Step 3 : Use a protractor to draw the angle for each sector.
Step 4 : Label the circle graph and all its sectors.
Example:
In a school, there are 750 students in Year1, 420 students in Year 2 and 630
students in Year 3. Draw a circle graph to represent the numbers of students in
these groups.
Solution:
Total number of students = 𝟕𝟓𝟎 + 𝟒𝟐𝟎 + 𝟔𝟑𝟎 = 𝟏, 𝟖𝟎𝟎.
𝒀𝒆𝒂𝒓 𝟏 𝒔𝒊𝒛𝒆 𝒐𝒇 𝒂𝒏𝒈𝒍𝒆 =
= 𝟏𝟓𝟎𝟎
𝒀𝒆𝒂𝒓 𝟐 𝒔𝒊𝒛𝒆 𝒐𝒇 𝒂𝒏𝒈𝒍𝒆 =
= 𝟖𝟒𝟎
𝒀𝒆𝒂𝒓 𝟑 𝒔𝒊𝒛𝒆 𝒐𝒇 𝒂𝒏𝒈𝒍𝒆 =
= 𝟏𝟐𝟔𝟎
𝟕𝟓𝟎
× 𝟑𝟔𝟎𝒐
𝟏𝟖𝟎𝟎
𝟒𝟐𝟎
× 𝟑𝟔𝟎𝒐
𝟏𝟖𝟎𝟎
𝟔𝟑𝟎
× 𝟑𝟔𝟎𝒐
𝟏𝟖𝟎𝟎
Similarly we can interpret the pie chart as in given word problems
Example:
This pie chart shows the results of a survey that
was carried out to find out how students travel to
school.
a) What is the most common method of
travel?
b) What fraction of the students travel to
school by car?
c) If 6 students travel by car, how many
people took part in the survey?
Example
A supermarket chain sold 3600 packets of sausages
last month.
The pie chart shows the different flavours.
a) How many packets of vegetarian sausages were
sold?
b) How many packets of beef sausages were sold?
Word Problem 1
A community centre organized a racial harmony fair
through which it collected a sum of $5880. The pie chart below shows the
amount of money collected by the various stalls.
a Find the sum of money collected by the games stall.
1
× $5880 = $1470
4
The games stall collected $1470.
b) What percentage of the total money was collected by the souvenir stall?
$5880 − $882 − $2352 − $1470 = $1176
The souvenir stall collected $1176.
$1176
× 100% = 20%
$5880
The souvenir stall collected 20% of the total money.
c) What fraction of the total money was collected by the foods stall?
$2352
2
=
$5880
5
2
of the total money was collected by the foods stall.
5
d) What fraction of the total money was collected by the drinks stall?
$882
3
=
$5880
20
3
of the total money was collected by the drinks stall.
20
e) What percentage of the total money was collected by the food and drinks
stalls?
$2352 + $882 = $3234
The food and drinks stalls collected $3234 together.
$3234
× 100% = 55%
$5880
55% of the total money was collected by the food and drinks stalls.
f) What was the ratio of the sum of money collected by the food and drinks
stalls to the sum of money collected by the games stall?
$3234 : $1470 = 11 : 5
The ratio of of the sum of money collected by the food and drinks stalls to
the sum of money collected by the games stall was 11 : 5.
Word Problem 2
A clothing merchant has 3840 pieces of clothing of 5 types. The pie chart below represents what fraction of the
clothing are of each type. PQ is the diameter of the circle on the pie chart.
a) How many shirts does the clothing merchant have?
1 3
−
2 8
4−3
8
1
=
8
=
1
× 3840 = 480
8
The clothing merchant has 480 shirts.
b) What fraction of the clothing are dresses?
1
1
1
10 − 2 − 5
−
−
=
2
5
4
20
3
=
20
3
of the clothing are dresses.
20
c) How many dresses are there?
3
× 3840 = 576
20
There are 576 dresses.
d) Are there more dresses or skirts? How many more?
From the pie chart it is clear that there are more skirts than dresses (as the pie
representing the skirts is bigger than the pie representing the dresses).
1
× 3840 = 768
5
There are 768 skirts.
768 − 576 = 192
There are 192 more skirts than dresses.
e) What is the ratio of the number of T-shirts to the number of shirts?
3
× 3840 = 1440
8
There are 1440 T-shirts.
1440 : 480 = 3 : 1
The ratio of the number of T-shirts to the number of shirts
is 3 : 1.
f) How many percent of the clothing are pants and skirts?
1
× 3840 = 960
4
There are 960 pairs of pants.
960 + 768 = 1728
There are 1728 pants and skirts together.
1728
× 100 = 45%
3840
45% of the clothing are pants and skirts.
Word Problem 3
A florist has some roses in 5 different colours. The pie chart below shows what
percentage of the roses are in each colour. AB is a diameter of the circle on the
pie chart.
a) How many percent of the roses are orange?
50% − 25% − 12% = 13%
13% of the roses are orange.
b) Given that there are 36 yellow roses, how many roses are there altogether?
12%
36
1%
36
12
= 3
100%
3 × 100
= 300
There are 300 roses altogether.
c) What is the ratio of the number of white roses to the number of red roses?
50% − 40% = 10%
10% of the roses are white.
10
× 300 = 30
100
There are 30 white roses.
40% of the roses are red.
40
× 300 = 120
100
There are 120 red roses.
30 : 120 = 1 : 4
The ratio of the number of white roses to the number of red roses is 1 : 4.
Self think Question
The following pie-chart shows the percentage distribution of the expenditure
incurred in publishing a book.
Study the pie-chart and the
answer the questions based on
it.Various Expenditures (in percentage)
Incurred in Publishing a Book
a) If for a certain quantity of
books, the publisher has to pay
Rs. 30,600 as printing cost,
then what will be amount of
royalty to be paid for these books?
Ans: 𝒓 = 𝑹𝒔. 𝟐𝟐𝟗𝟓𝟎
b) What is the central angle of the sector corresponding to the expenditure
incurred on Royalty?
Ans: 54 degree
c) The price of the book is marked 20% above the C.P. If the marked price of the
book is Rs. 180, then what is the cost of the paper used in a single copy of the
book?
Ans: Rs 37.50
d) If 5500 copies are published and the transportation cost on them amounts to
Rs. 82500, then what should be the selling price of the book so that the
publisher can earn a profit of 25%?
Ans: Rs. 187.50
e) Royalty on the book is less than the printing cost by:
Ans: 25%
Practice Questions
Q1.
Mr. Sobieski asked his class to vote on where they would most like to go
on a field trip. The
choices he gave
them
were:
history museum,
science museum,
art gallery, and
nature preserve.
All 30 students
cast one vote
each. The pie
graph
below
shows the results.
Complete the table below to show how many votes each choice received.
a) How many more students chose the history museum than the science
museum?
b) How many students chose the nature preserve or the art gallery?
Q2.
A
popular
magazine took a
survey among
the readers on
their
favorite
entertainment.
The results were
published in a
circle graph. Use
the graph to
answer
the
questions.
a)
b)
c)
d)
e)
What fraction of readers chose watching TV as their favorite?
What fraction of readers likes to surf the Internet?
What are the two forms of entertainment equally liked?
What fraction of people prefer going to movies?
Which entertainment is the most popular among the readers?
Q3.
A sweet shop sells four flavours of ice cream: vanilla, chocolate, strawberry
and mint. The pie chart shows the percentage of each sold in one day.
b) If 400 ice creams were sold altogether, how many were Vanilla?
c) If 400 ice creams were sold altogether, how many were strawberry?
Q4. This pie chart shows the Mc Creedy's household weekly expenditure,
broken down into categories:
b) If their expenditure on food is $300 per week, what is the weekly
expenditure on transport?
c) What is the expenditure of power?
d) What percentage of the family's income is spent on Power?
e) What is the percentage of expenditure of transport?
f) What is the daily expenditure of clothes
g) What is the fraction of weekly expenditure of power and transport?
h) Which one having the highest expenditure and which one is the least
expenditure?
Q5. The pie chart shows the
amount of time each day
that Jethro spends on
various activities.
a) What is the angle for the
sector of the pie chart
representing the time he
spends playing sport?
Q6. Anna did a survey where
she asked all the children in
her school to name their
favorite pet. The results are
shown in the pie chart:
a) If there were 800
children in the school,
how many said their
favorite pet was Fish?
b) If 720 children said their
favorite pet was a Dog,
how many children said
their favorite pet was a
Rabbit?
c) What is the angle for the
sector of the pie chart representing Fish?
Pie chart Practice from book:
a) Example on Page 302
b) Example3,4 on page 303
c) Q1,2 on page 304
d) Q3, 4, 5 on page 305
e) Q7, 8, 9, 10 on page 306
f) Q2 on page 322
g) Q7 on page 323
h) Q5 on page 325
i) Q3,8 on page 327
j) Q7 on page 330
Muhammad Javed Iqbal
Senior Teacher-1
FGS