Circle graphs

Learning Objectives Define the key geometric components of a circle graph, including sector, central angle, and arc. Calculate the central angle of a sector given a percentage or fraction of the total data. Determine the percentage of data represented by a sector, given its central angle. Calculate the area of a sector in a circle graph using the radius and central angle. Calculate the arc length of a sector in a circle graph using the radius and central angle. Construct an accurate circle graph from a given data set by calculating all necessary angles. Interpret data presented in circle graphs to solve multi-step, real-world problems. How do businesses show their market share or governments display budget allocations in a simple, visual way? 📊 They use the power of circl...

TermDefinitionExample Circle Graph (Pie Chart)A circular statistical graphic divided into sectors, or 'slices', to illustrate the numerical proportion of a whole. The entire circle represents 100% of the data.A chart showing that 50% of students prefer pizza, 25% prefer burgers, and 25% prefer tacos. The chart would be a circle with three slices. SectorThe region of a circle enclosed by two radii and the arc that connects them. Each 'slice' of a circle graph is a sector.In a pizza, a single slice is a sector of the whole pizza. Central Angle (θ)An angle whose vertex is the center of a circle and whose sides are two radii. The sum of all central angles in a circle graph is 360°.If a sector represents 25% of the data, its central angle is 25% of 360°, which is 90°. ArcA...

Central Angle Calculation \text{Central Angle } (\theta) = \frac{\text{Part}}{\text{Whole}} \times 360^\circ Use this formula to convert a fraction, decimal, or percentage of the data into the corresponding central angle for its sector. For a percentage, the formula is simply \text{Percentage (as decimal)} \times 360^\circ. Sector Area Formula \text{Area}_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2 Use this formula to calculate the area of a single slice (sector) of a circle graph, where \theta is the central angle of the sector and r is the radius of the circle. Arc Length Formula \text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r Use this formula to calculate the length of the outer curved edge (arc) of a sector, where \theta is the central an...