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MATHS 5 Marks Questions

Pie Charts · UP Board (UPMSP) STD 8 (UPMSP - English Medium). 10 questions.

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5 Marks Questions

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10 questions · timed · auto-graded

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^\circ $
Food $10800$ $135^\circ $
Clothing $5600$ $70^\circ $
Education $3600$ $45^\circ $
Savings $800$ $10^\circ $
Construction of pie chart: Steps of construction$-$
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $100^\circ , 135^\circ , 70^\circ , 45^\circ $ and $10^\circ .$
$iv.$ 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^\circ $
$B$
$40$
$144^\circ $
$C$
$25$
$90^\circ $
$D$ $15$
$54^\circ $
Construction of pie chart: Steps of construction-
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $72^\circ , 144^\circ , 90^\circ $ and $54^\circ .$
$iv.$ 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^\circ $
Second division
$45$
$162^\circ $
Third division
$20$
$72^\circ $
Failed $10$
$36^\circ $
Construction of pie chart: Steps of construction-
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $90^\circ , 162^\circ , 72^\circ $ and $36^\circ .$
$iv.$ 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^\circ $
Muslim
$270$
$90^\circ $
Sikh
$255$
$85^\circ $
Christian
$105$
$35^\circ $
Construction of pie chart: Steps of construction-
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $150^\circ , 90^\circ , 85^\circ $ and $35^\circ .$
$iv.$ 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^\circ $
Private bus
$245$
$70^\circ $
Bicycle
$210$
$60^\circ $
Rickshaw
$175$
$50^\circ $
On foot
$280$
$80^\circ $
Construction of pie chart: Steps of construction$-$
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $100^\circ , 70^\circ , 60^\circ , 50^\circ $ and $80^\circ .$
$iv.$ 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^\circ $
Hindi
$75$
$50^\circ $
Mathematics
$150$
$100^\circ $
Science $120$
$80^\circ $
Social science $90$ $60^\circ $
Construction of pie chart: Steps of construction$-$
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $70^\circ , 50^\circ , 100^\circ , 80^\circ $ and $60^\circ .$
$iv.$ 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^\circ $
Wheat
$76$
$144^\circ $
Coarse cereals
$38$
$72^\circ $
Pulses $19$
$36^\circ $
Construction of pie chart: Steps of construction$-$
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $108^\circ , 144^\circ , 72^\circ $ and $36^\circ .$
$iv.$ 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 $= (26 + 30 + 21 + 5 + 8) = 90$
Central 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^\circ $
Apples
$30$
$120^\circ $
Oranges
$21$
$84^\circ $
Coconuts $5$
$20^\circ $
Pomegranates $8$ $32^\circ $
Construction of pie chart: Steps of construction$-$
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $104^\circ , 120^\circ , 84^\circ , 20^\circ $ and $32^\circ .$
$iv.$ 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^\circ $
Home work
$4$
$60^\circ $
Play
$2$
$30^\circ $
Sleep
$8$
$120^\circ $
Others
$3$
$45^\circ $
Construction of pie chart: Steps of construction$-$
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $105^\circ , 60^\circ , 30^\circ , 120^\circ $ and $40^\circ .$
$iv.$ 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^\circ $
Other land animals
$400$
$160^\circ $
Birds
$175$
$70^\circ $
Water animals
$125$
$50^\circ $
Reptiles
$50$
$20^\circ $
Construction of pie chart: Steps of construction-
$i.$ Draw a circle of any convenient radius.
$ii.$ Draw a horizontal radius of this circle.
$iii.$ Draw sectors whose central angles are $60^\circ , 160^\circ , 70^\circ , 50^\circ $ and $20^\circ .$
$iv.$ 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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