Question

The pie chart shows the distribution of the grades obtained by the groups of the students in a test. The number of students who scored grade C is twice the number who scored grade B, and
$\dfrac{3}{5}$ of the students scored grade B and grade C. Find the angle of the sector which represents grade C.

Answer 1

Hint: Since we know that pie char represents the percentage or proportion data in the form of the angle ratios. To find the angle of the sector which represent grade C, we will first find the fraction of the students who scored grade C. Let us assume that there are ‘x’ students in the class and ‘C’ be the number of students who scored grade C and ‘B’ be the number of students who scored grade B.

Complete step by step answer:
Then, from question, we know that number of students who scored grade C is twice the number of students who scored grade B. (i.e.)
C =2B------(1)
And, $\dfrac{3}{5}$ of the students scored grade B and grade C, that is:
B + C = $\dfrac{3}{5}x$---------(2)
We will solve both the above equation and find the value fraction of the total students who scored grade C. Then, the angle of the sector which represents grade C is equal to the angle made by the circle at the center multiplied by the fraction of total students who scored grade C.


We know that the pie chart represents the percentage or proportion data in the form of the angle ratios. So, to find the angle of the sector, which represents grades C we have to first find the fraction of students who scored grade C.
Now, let us say that there are ‘x’ students in the class and ‘C’ be the number of students who scored grade C and ‘B’ be the number of students who scored grade B.
Now, in the question it is given that number of students who scored grade C is twice the number of students who scored grade B. Hence, we can write it as:
C =2B……………..(1)
And, the total number of students who scored grade B and grade C is $\dfrac{3}{5}$ of total students.
Hence, we can write it as:
B + C = $\dfrac{3}{5}x$…………………(2)
Now, we will put the value of C from equation (1) to equation (2), then we will get:
2B +B = $\dfrac{3}{5}x$
$\Rightarrow 3B=\dfrac{3}{5}x$
$\therefore B=\dfrac{1}{5}x$
Hence, from equation (1) we can say that:
C = $\dfrac{2}{5}x$
Hence, the fraction of students who scored grade C $\dfrac{2}{5}$ of the total students.
We know that the total angle made by the circle at the center is equal to $360{}^\circ $. Hence, the angle made by sector which represents grade C will be $\dfrac{2}{5}$of the total angle (i.e. $360{}^\circ $).
So, the angle of the sector which represent grade C is equal to:$\dfrac{2}{5}\times 360{}^\circ $$=72{}^\circ \times 2$$=144{}^\circ $
Hence, the angle made by the sector at the center of the pie chart which represents grade C is $144{}^\circ $.
This is our required solution.

Note:
 Students are required to note that each slice of the pie represents the fraction or the proportion of that particular item in the whole collection of different items which it is representing. So, the angle of the sector which represents that item is equivalent to the fraction of the total items that particular slice is representing.