a A circle graph is appropriate to represent the data in the table because the percentages add up to 100 % and we can use an entire circle.
Method
Percent of students
Bus
65 %
Walk
25 %
Other
10 %
b Let's begin by drawing a circle with a radius of 2 inches.
We have to divide this circle into three sectors of different sizes to represent the data given in the table. To do that, we need to find the central angle used for each sector.
Method
Percent of students
Bus
65 %
Walk
25 %
Other
10 %
Because 65 % of the students get to school using a bus, the central angle is equal to 65 % multiplied by 360^(∘).
65 % * 360^(∘) = 0.65* 360^(∘) = 234^(∘)
From the above, the sector that will represent the percent of students going to school in bus has a central angle of 234^(∘). Similarly, let's find the central angles of the other two sectors.
Method
Percent of students
Central angle
Bus
65 %
64 % * 360^(∘) = 234^(∘)
Walk
25 %
25 % * 360^(∘) = 90^(∘)
Other
10 %
10 % * 360^(∘) = 36^(∘)
Finally, let's make a graph representing the data in the table.
c In this part, we will find the area of each sector drawn in Part B. Let's label some points on it and mark the central angles.
To find the area of a sector, we will use the formula below.
Area of a sector = mAB/360^(∘)* π r^2
Let's substitute the corresponding values into the formula above.
