 So we want to learn the applications of pie chart. So let's say there is a problem and wherein we have been given that 90 students play different sport in a school and these sports are given as cricket, basketball, chess, badminton, football and these 90 students play one of these sports and the distribution of how they play the sport or how many students play a particular sport is given by this particular pie diagram. Now we want to find out how many students play each of the sport from the pie chart. We see that there are different sectors that every sport corresponds to and I have coded them in colors. For example, this green refers to cricket and this substance 56 degrees of central angle and similarly chess has a purple color and it's up to 40 degrees of the central angle. Now using this pie diagram or pie chart, how can we find out how many students play a specific sport? For example, cricket or badminton or football. We know that the total number of students are 90 and if we wanted to find out how many play cricket, we will look at the central angle of that sector, which is a green sector which subtends 56 degrees of the angle. The total circle refers to 360 degrees. So I'll just quickly write it down. Total circle refers to 360 degrees of the central angle. So let's just assume that every if everybody played cricket. So the circle would all be green and the central angle that will correspond to that sector will be of 360 degrees. So if all the 90 students played cricket, the central angle would be 360 degrees, but here it's not 360 degrees but rather 56 degrees. So the fraction of students playing cricket out of 90 students is 56 degrees divided by 360 degrees, which is nothing but again fraction of students playing cricket and how much is this fraction and this fraction is exactly 56 degrees divided by 360 degrees. It should also be equal to number of students which play cricket and I'll just write C as an unknown divided by 90 because total number of students is 90 and out of those some C students play cricket. So what we have is this equation 56 divided by 360 equal to C by 90. So I'll just quickly write it here again and now we need to solve this equation for C. So if we multiply both sides by 90 we get 90 times 56 divided by 360 is equal to C 360 is 4 times 90. So we will have 4 in the denominator and then we can divide 56 by 4 to get 14 and therefore 14 students play cricket. We can find out values for all these numbers. So let's quickly solve all these numbers for how many students play basketball, chess, badminton, football, etc. and we will have some practice over this. So let's use color for basketball, which is kind of a light, it's kind of a light skin color. So the central angle that this sector here makes is 4 degrees 4 degrees divided by 360 degrees should be equal to number of students which play basketball. I'll write it as B divided by 90 and so we can multiply both sides by 90. We have 90 times 4 degrees divided by 360 degrees and so this gives us B is equal to 1. So only one student plays basketball. This is so weird. I don't know with who this student is playing basketball with, but this is a little funny. Anyway, let's go ahead. Let's go for the purple color and in purple color we have chess. Let's see how many students are interested in chess. So 40, which is the angle in degrees, which is a central angle divided by 360 degrees equal to I'll write C H for the unknown and C H divided by 90 multiplying both sides by 90. We can get the value of C H as 10 and so 10 students are interested in chess. Let's go for badminton now and the angle that this orange sector substance at the center is 36 degrees. So divided by 360 degrees shows us the fraction of students playing badminton. I'll just write bad instead of writing badminton. Let's just write M for badminton and divided by 90, which is total number of students and how we can solve this is by isolating M by multiplying both sides by 90. So we get M is equal to 36 degrees times 90 divided by 360 degrees. We have this as nine. So M is equal to nine. This means nine students play badminton. We can clearly see that this pink color shows number of students playing football, but we don't know the central angle. This is a little tricky, but now because we know that a total central angle for the circle is 360 degrees. Let's just add all the central angles that are given to us and subtract that from 360 degrees. So 360 degrees minus in bracket 36 degrees plus 40 degrees plus 56 degrees will give us the central angle for the football and this central angle for football comes out to be 360 degrees. Sorry 360 degrees minus 136 degrees, which is nothing but 224 degrees. So the central angle is 224 degrees. Now the number of students playing football would be 224 divided by 360 degrees equal to using the unknown F in the numerator, which is the number of students playing football divided by total number of students. So to isolate F we will multiply both sides by 90. We can quickly complete this computation to give us F which comes out to be 56. So out of 90 students almost 56 students are interested in football and this is how just by looking at the central angle in the pie diagram, we are able to find out the actual values when the total number of students has been given to us.