5 Marks Questions

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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