 A slice of pizza has a radius of 9 inches. It forms an angle of 30 degrees at the centre. Find the area of the slice. So we need to figure out this area of the slice using this information. So how do we go about this? So we can think of this slice as a part of a big circular pizza. So this slice is actually a sector of that big circular pizza. We already know what a sector of a circle is but just as a refresher let me bring the big circular pizza here. So this slice of pizza is actually a part of this circular pizza. Now if I divide this pizza into slices like this then each of the slices here is actually a sector of the pizza. So let's say if I take this slice over here then this slice is a sector of the circle. So the radius of slice means the radius of this circle. So the radius of the circle is 9 inches which is also the radius of the slice and this sector makes an angle of 30 degrees at the centre which is the centre of the circle. Now we need to figure out the area of this sector over here. Now we already know that a full circle makes an angle of 360 degrees at its centre and the area covered by a complete circle is pi r squared. So we can say that in 360 degrees a circle would cover an area of pi r squared. So how much area would a circle cover if it makes 1 degree angle at its centre? So the area covered should be pi r squared times 1 degree divided by 360 degrees. So the area covered by this sector which makes an angle of 30 degrees at the centre should be pi r squared times 30 degrees, 30 degrees divided by 360 degrees. Now we already know the value of r so we can put it here, let's do that. So this would be equal to pi times the value of r is 9 inches. So 9 times 9 times 30 degrees divided by 360 degrees. So how much is this? So 30 times 12 is 360, 3 times 3 is 9, 3 times 4 is 12. So this is equal to 9 times 3 times pi which is 27 pi by 4 inches square. So the area of our pizza slice is 27 pi by 4 inches square. So this is how we find the area of any sector of a circle and sometimes in your textbook you will see a formula which is nothing but a generalized version of this process. And let me put that down as well for you. So let's say we have a sector which makes an angle of theta at the centre. So the area of this sector, the area of this sector which makes an angle of theta at the centre would be equal to the area of our circle which is pi r squared times the angle made by the sector theta divided by the total angle made by the circle which is 360 degrees. So this is the formula we generally see in our textbooks which is nothing but a generalized version of this process.