00:01
In this problem we are given an illustration for the wedge of a plate that i will trace out in red and we want to calculate its perimeter and area as a function of variables alpha for the opening angle here, pi, and the radius.
00:26
The radius is the radius of the circle but our length here of the wedge is 2r.
00:36
Let's start with the perimeter.
00:38
The perimeter p will be given by the sums of each of our lengths here where this length here is 2r, this length here is another 2r, plus the arc length here and general speaking an arc length l is given by r times theta where theta is in radians and we have the radius and we have alpha, the radius, so this will be given by 2r alpha.
01:12
Again, why 2r here is because our length is defined as twice the radius of the circle.
01:17
Slightly confusing or annoying but we're just following procedure here.
01:23
So our perimeter will simplify to 4r plus 2r alpha or you can write it as 2r times 2 plus alpha.
01:40
Now let's find the area.
01:45
So the area of a wedge here, we can find it by recalling that the area of a circle, the area of the total circle is equal to pi r squared.
02:08
But we don't want the area of the total circle, we only want the area of the wedge which will be equal to the area of the circle, pi r squared, times the ratio of our angle here, alpha and radians, over 2 pi.
02:27
2 pi for the radians of an entire circle...