RS Aggarwal Class 8 Mathematics Solutions Chapter 23 Pie Charts

Question 1. Look at the pie chart to compare the results. Which was the most popular sport? Which was the least popular?
Answer: According to the pie chart showing favourite sports, football was the most popular sport with 7 people choosing it. Cricket was the least popular sport with only 1 person selecting it.
In simple words: Football had the biggest slice in the pie chart, so the most people picked it. Cricket had the smallest slice, so the fewest people chose it.

Exam Tip: When reading pie charts, always compare the sizes of the sectors - larger sectors represent more popular or higher values. Look at the legend to confirm which colour matches which category.

Question 2. [Pie chart construction question - determine the central angles and construct the pie chart for expenditure data]
Answer: First, determine the central angle for each expenditure category using the formula: central angle = (value of component / total value) × 360°. For the given expenditure data with total of Rs 14,400, the central angles are: Rent 100°, Food 135°, Clothing 70°, Education 45°, and Savings 10°. Draw a circle and mark a horizontal radius. Starting from this radius, draw sectors with these central angles in sequence. Shade and label each sector with its category name. The resulting pie chart shows the relative proportions of each expenditure type.
In simple words: Divide the total amount by 360 degrees to find how many degrees each rupee represents. Multiply each expense by this rate to get its angle. Then draw the pie chart using these angles.

Exam Tip: Always verify that all central angles add up to exactly 360° before drawing. Use a protractor carefully to ensure angles are accurate, and label every sector clearly.

Question 3. [Pie chart construction question - determine the central angles and construct the pie chart for creatures data]
Answer: With a total of 900 creatures, find the central angle for each type using: central angle = (number of creatures of that type / 900) × 360°. The central angles are: Beast animals 60°, Other land animals 160°, Birds 70°, Water animals 50°, and Reptiles 20°. Draw a circle with a horizontal radius. From this radius, draw sectors with the calculated central angles in sequence. Shade each sector differently and add labels identifying each creature type. This pie chart visually displays the distribution of creatures across the five categories.
In simple words: Find what fraction each creature type is of the total. Multiply that fraction by 360° to get the angle for its pie slice. Draw and shade each slice, then label it.

Exam Tip: Double-check your angle calculations by ensuring the sum equals 360°. Use different colours or shading patterns to make each sector visually distinct, which helps readers quickly identify categories.

Question 4. [Pie chart construction question - determine the central angles and construct the pie chart for student transport data]
Answer: With 1,260 students total, calculate the central angle for each transport mode: central angle = (number of students using that mode / 1,260) × 360°. The angles are: School bus 100°, Private bus 70°, Bicycle 60°, Rickshaw 50°, and On foot 80°. Create a circle and draw a horizontal radius. From this starting radius, draw sectors representing each mode using the calculated angles. Shade and label all sectors to show how students travel to school. The completed pie chart illustrates the transport method distribution across the entire student population.
In simple words: For each transport mode, divide the number of students by 1,260 and multiply by 360. This gives the angle for that mode's slice. Draw all slices from the same centre point, shade them, and add labels.

Exam Tip: When multiple questions use similar methods, list all calculations in a clear table format before drawing - this prevents errors and makes verification easier for examiners.

Question 5. [Pie chart construction question - determine the central angles and construct the pie chart for religious community data]
Answer: Given 1,080 workers total, determine the central angle for each religion using: central angle = (workers in that religion / 1,080) × 360°. The central angles are: Hindu 150°, Muslim 90°, Sikh 85°, and Christian 35°. Draw a circle and begin with a horizontal radius. Moving clockwise or counterclockwise, draw sectors for each religion using these angles. Apply different shades or colours to each sector and label them clearly. The pie chart displays the religious composition of the workforce in a visually comparable format.
In simple words: Divide each religion's number by the total, then multiply by 360° to find its angle. Use a protractor to draw each sector from the centre, making sure all angles together equal 360°.

Exam Tip: Label sectors inside or outside the pie based on available space, but always use clear leader lines if labelling outside. Ensure the legend matches the pie chart colours exactly.

Question 6. [Pie chart construction question - determine the central angles and construct the pie chart for subject marks data]
Answer: With total marks of 540, find the central angle for each subject: central angle = (marks obtained in that subject / 540) × 360°. The angles are: English 70°, Hindi 50°, Mathematics 100°, Science 80°, and Social science 60°. Start by drawing a circle and marking a horizontal radius. Draw sectors from this radius using the calculated angles, moving around the circle. Shade and label each sector to identify the subject. The resulting pie chart compares performance across all five subjects, showing which subject had the highest and lowest marks visually.
In simple words: Each subject's marks divided by 540, multiplied by 360°, gives its slice angle. Draw the pie by measuring these angles with a protractor and colouring each subject differently.

Exam Tip: For academic pie charts, always list the marks and angles in a calculation table first. This shows your working clearly and helps spot arithmetic errors before you start drawing.

Question 8. [Pie chart construction question - determine the central angles and construct the pie chart for fruit data]
Answer: With a total of 90 fruits, find the central angle for each type: central angle = (number of each fruit type / 90) × 360°. The central angles are: Mangoes 104°, Apples 120°, Oranges 84°, Coconuts 20°, and Pomegranates 32°. Draw a circle and start with a horizontal radius. From this radius, draw sectors using the calculated angles, moving around the circle. Shade each sector with a distinct colour or pattern and label it with the fruit name. The pie chart clearly shows which fruit type is most abundant (Apples with 30 fruits) and which is least common (Coconuts with 5 fruits).
In simple words: Divide each fruit's count by 90 and multiply by 360° to get its angle. Draw the pie using these angles, shade differently, and label each slice.

Exam Tip: Always check that your angles sum to 360° to catch calculation errors early. When drawing, start from the same horizontal radius for consistency.

Question 9. [Pie chart construction question - determine the central angles and construct the pie chart for food grain production data]
Answer: Given total production of 190 million tonnes, the central angle for each food grain is: central angle = (production of that grain / 190) × 360°. The angles are: Rice 108°, Wheat 144°, Coarse cereals 72°, and Pulses 36°. Create a circle and draw a horizontal radius. Starting from this radius, construct sectors using these angles going around the circle. Shade and label each sector to represent the respective food grain. The pie chart illustrates that wheat is the most produced grain at 76 million tonnes (144°), while pulses have the lowest production at 19 million tonnes (36°).
In simple words: For each grain, find its production divided by 190, then multiply by 360° for the slice angle. Draw the pie chart using a protractor to measure these angles accurately.

Exam Tip: In agriculture-based pie charts, note which crop dominates production - this often reflects regional climate and farming practices. Ensure all labels are legible by using external labelling with leader lines if needed.

Question 10. [Pie chart construction question - determine the central angles and construct the pie chart for exam results data]
Answer: With a total of 100%, find the central angle for each category: central angle = (percentage value / 100) × 360°. The central angles are: First division 90°, Second division 162°, Third division 72°, and Failed 36°. Draw a circle and mark a horizontal radius. Starting from this radius, draw sectors using the calculated angles in sequence. Shade and label each sector to identify the exam result category. The completed pie chart shows that Second division is the most common result at 45% (162°), while First division at 25% (90°) indicates fewer students achieved the highest marks, and Failed at 10% (36°) represents the smallest group.
In simple words: Since the percentages add to 100%, divide each by 100 and multiply by 360° to find the angle. Draw sectors for First division, Second division, Third division, and Failed using these angles.

Exam Tip: For percentage-based pie charts, verify that all percentages sum to 100% before starting calculations. Always start from the horizontal radius and move consistently in one direction around the circle.

Question 11. [Pie chart construction question - determine the central angles and construct the pie chart for brand buyers data]
Answer: Given that the total percentage is 100%, calculate the central angle for each brand: central angle = (percentage of buyers / 100) × 360°. The central angles are: Brand A 72°, Brand B 144°, Brand C 90°, and Brand D 54°. Draw a circle and establish a horizontal radius as the starting point. From this radius, draw sectors corresponding to each brand using the calculated angles. Shade and label each sector to show which brand it represents. The pie chart reveals that Brand B dominates with 40% market share (144°), while Brand D has the smallest share at 15% (54°).
In simple words: Divide each brand's percentage by 100 and multiply by 360° to find its angle. Use a protractor to draw each sector, shade it, and label the brand name.

Exam Tip: For market share pie charts, highlight the dominant and weakest players in your analysis. Always ensure sectors are clearly distinguished through colour or shading for easy interpretation.

Question 12. [Pie chart question - calculate central angle for a specific component]
Answer: To find the central angle of the sector representing travel expenses from a monthly income breakdown, apply the formula: central angle = (value of travel expenses / monthly income) × 360°. Based on the given data where travel expenses are 250 and monthly income is 2400, the calculation is: (250 / 2400) × 360° = (250 × 360°) / 2400 = 37.5°. This means the sector representing travel expenses in the pie chart has a central angle of 37.5°, or \( 37\frac{1}{2}° \). This sector occupies approximately 10.4% of the total pie, indicating the proportion of monthly income allocated to travel.
In simple words: Divide the travel cost by the total monthly income, then multiply by 360° to find the angle of its pie slice.

Exam Tip: When the calculation gives a decimal or fractional angle, express it in both decimal and fraction form (e.g., 37.5° or \( 37\frac{1}{2}° \)). Always show the complete formula and intermediate steps.

Question 13. [Pie chart question - calculate central angle for a specific component]
Answer: To find the central angle of the sector representing the Sikh community from a pie chart showing religious distribution, use the formula: central angle = (percentage value of that group / 100) × 360°. For a Sikh community representing 35% of the total population, the calculation becomes: (35 / 100) × 360° = 126°. Thus, the sector for the Sikh community has a central angle of 126°. This sector takes up 35% of the entire pie, clearly showing the religious composition and the proportion the Sikh community holds in the total population.
In simple words: If the Sikh community is 35% of the total, find what angle represents 35% of 360°. Divide 35 by 100 and multiply by 360° to get 126°.

Exam Tip: Always verify your angle by checking that (angle / 360°) equals the given percentage when converted to decimal form. This reverse calculation confirms accuracy.

Question 14. [Pie chart question - find the total quantity given a central angle and partial value]
Answer: Let the total number of students be x. If a sector with central angle 48° represents students who opted for arts stream, then apply the relationship: (x / 1650) × 360° = 48°, where 1650 is derived from context. Solving: (360x) / 1650 = 48, which gives 360x = 48 × 1650 = 79,200, so x = 79,200 / 360 = 220. Therefore, 220 students opted for the arts stream. This calculation demonstrates how to work backwards from a known central angle and total to find the number of students in a specific category.
In simple words: If an angle of 48° represents some students out of a total, set up the equation (total / all students) × 360° = 48°. Solve for the total to find how many students chose arts.

Exam Tip: When reversing the pie chart calculation, always rearrange the formula carefully and double-check by substituting your answer back into the original relationship.

Question 15. [Introduction to pie charts - define and explain the concept]
Answer: A pie chart is a circular statistical graphic divided into slices or sectors, where each slice represents a proportion or percentage of the total. The chart gets its name from its resemblance to a sliced pie. Pie charts are used to display and compare information across different categories, making it easy to see which items are most and least significant at a glance. From geometry, we know that the complete angle around a circle's centre is 360°. The area of each sector is proportional to the value it represents, and the central angle of each sector can be calculated using the formula: central angle = (component value / total value) × 360°. To convert an angle to a percentage, use: percentage = (angle / 360°) × 100%. Pie charts are widely used in surveys, business reports, demographic studies, and educational materials to present data in an easily understandable visual format.
In simple words: A pie chart is like a pizza cut into slices, where each slice shows a different part of the whole. Bigger slices mean bigger amounts. Use the 360° of the circle to figure out how big each slice should be.

Exam Tip: Always remember that pie charts work because 360° represents the complete circle - this is why the formula uses 360 as the denominator. Use this fact to check all your calculations.