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Maths 5 Mark Question

Pie Charts · Maharashtra Board STD 8 (MSBSHSE - Semi English Medium). 10 questions.

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5 Mark Question

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10 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 Marks
The monthly income of family is ₹ 28800. The monthly expenditure of the family on various items is given below.
Item Rent Food Clothing Education Saving
Expenditure (in ₹) 8000 10800 5600 3600 800
Represent the above data by a pie chart.
Answer
Monthly income of the family = ₹ 28,800
Central angle for each item $=\Big(\frac{\text{Expenditure per month on various items}}{\text{Monthly income}}\times360\Big)^\circ$
Calculation of central angles,
Items Expenditure (in ₹) Central angle
Rent 8000 100°
Food 10800 135°
Clothing 5600 70°
Education 3600 45°
Savings 800 10°
Construction of pie chart:
Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 100°, 135°, 70°, 45° and 10°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, the pie chart is obtained as follows.
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Question 25 Marks
The following table shows the percentages of buyers of four different brands of bathing soaps.
Brand
 A B C D
Percentage of buyers
20%
40%
 25%
15%
Represent the above data by a pie chart.
Answer
Total percentage = 100 Central angle for each category $=\Big(\frac{\text{value(in\%)of each brand}}{\text{100}}\times360\Big)^\circ$ Calculation of central angles,
Brand
Buyers (in %)
Central angle
A
20
72°
B
40
144°
C
25
90°
D 15
54°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 72°, 144°, 90° and 54°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 35 Marks
Given below is the result of an annual examination of a class, showing the percentage of students in each category.
First division
Second division
Third division
Failed
25%
45%
20%
10%
Represent the above data by a pie chart.
Answer
Total percentage = 100 Central angle for each category $=\Big(\frac{\text{value(in%)of each category}}{\text{100}}\times360\Big)^\circ$ Calculation of central angles,
Category
Result (in %)
Central angle
First division
25
90°
Second division
45
162°
Third division
20
72°
Failed 10
36°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 90°, 162°, 72° and 36°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 45 Marks
The data on religion wise division of 1080 workers of a factory are given below:
Religion
Hindu
Muslim
Sikh
 Christian
Number of workers
450
270
255
 105
Draw a pie chart to represent the above data.
Answer
Total number of creatures = 1080 Central angle for each component$=\Big(\frac{\text{number of workers in each religion}}{\text{total number of workers}}\times360\Big)^\circ$ Calculation of central angles,
Religion
Marks obtained
Central angle
Hindu
450
150°
Muslim
270
90°
Sikh
255
85°
Christian
105
35°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 150°, 90°, 85° and 35°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 55 Marks
Various modes of transport used by 1260 students in a given school are given below:
School bus
Private bus
Bicycle
Rickshaw
On foot
350
245
210
175
280
Represent the above data by a pie chart.
Answer
Total number of creatures = 1260 Central angle for each component$=\Big(\frac{\text{number of creatures in each type}}{\text{total number of creatures}}\times360\Big)^\circ$ Calculation of central angles,
Mode of transport
Number of students
Central angle
School bus
350
100°
Private bus
245
70°
Bicycle
210
60°
Rickshaw
175
50°
On foot
280
80°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 100°, 70°, 60°, 50° and 80°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 65 Marks
The marks obtained by Sudhir in an examination are given below:
Subject
English
Hindi
Mathematics
Science
Social science
Marks obtained
105
75
150
120
90
Represent the above data by a pie chart.
Answer
Total number of obtained = (105 + 75 + 150 + 120 + 90) = 540 Central angle for each component$=\Big(\frac{\text{marks obtained in each subject}}{\text{total marks of obtained}}\times360\Big)^\circ$ Calculation of central angles,
Subject
Marks obtained
Central angle
English
105
70°
Hindi
75
50°
Mathematics
150
100°
Science 120
80°
Social science 90 60°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 70°, 50°, 100°, 80° and 60°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 75 Marks
The following data shows the agricultural production in India during a certain year.
Foodgrain
Rice
Wheat
Coarse cereals
Pulses
Production (in millions of tonnes)
57
76
38
19
Draw a pie chart to represent the above data.
Answer
Total production = (57 + 76 + 38 + 19) = 190 Central angle for each foodgrain $=\Big(\frac{\text{production of each foodgrain }}{\text{total production}}\times360\Big)^\circ$ Calculation of central angles,
Food grain
production (in millions of tonnes)
Central angle
Rice
57
108°
Wheat
76
144°
Coarse cereals
38
72°
Pulses 19
36°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 108°, 144°, 72° and 36°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 85 Marks
The marks obtained by Sudhir in an examination are given below:
Type of fruit
Mangoes
Apples
Oranges
Coconuts
Pomegranates
Number
26
30
21
5
8
Represent the above data by a pie chart.
Answer
Total number of fruits = (26 + 30 + 21 + 5 + 8) = 90Central angle for each component $=\Big(\frac{\text{number of each type of fruit}}{\text{total number of fruit}}\times360\Big)^\circ$
Calculation of central angles,
Types of fruit
Number
Central angle
Mangoes
26
104°
Apples
30
120°
Oranges
21
84°
Coconuts 5
20°
Pomegranates 8 32°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 104°, 120°, 84°, 20° and 32°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 95 Marks
The data given below shows number of hours spent by a school boy on different activities on a working day.
Activity
School
Homework
Play
 Sleep Others
Total
Number of hours
7
4
2
 8 3
24
Represent the above data by a pie chart.
Answer
Total number of creatures = 24 Central angle for each component$=\Big(\frac{\text{number of creatures in each type}}{\text{total number of creatures}}\times360\Big)^\circ$ Calculation of central angles,
Activity
Number of hours
Central angle
School
7
105°
Home work
4
60°
Play
2
30°
Sleep
8
120°
Others
3
45°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 105°, 60°, 30°, 120° and 40°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
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Question 105 Marks
The monthly income of family is ₹ 28800. The monthly expenditure of the family on various items is given below.
Beast animals
Other land animals
Birds
Water animals
Reptiles
150
400
175
125
50
Represent the above data by a pie chart.
Answer
Total number of creatures=900 Central angle for each component$=\Big(\frac{\text{number of creatures in each type}}{\text{total number of creatures}}\times360\Big)^\circ$ Calculation of central angles,
Creatures
Number of creatures
Central angle
Beast animals
150
60°
Other land animals
400
160°
Birds
175
70°
Water animals
125
50°
Reptiles
50
20°
Construction of pie chart: Steps of construction-
  1. Draw a circle of any convenient radius.
  2. Draw a horizontal radius of this circle.
  3. Draw sectors whose central angles are 60°, 160°, 70°, 50° and 20°.
  4. Shade the sectors so obtained differently and label each one of them.
Thus, we obtain the required pie chart as shown in the figure below.
View full question & answer→
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