WEBVTT
00:00:01.250 --> 00:00:05.890
The circle in the given figure has a radius π, and the angle of the sector is π.
00:00:06.500 --> 00:00:09.380
Write down an expression for the area of the circle.
00:00:09.820 --> 00:00:13.470
What fraction of the circle is the sector with central angle π?
00:00:13.870 --> 00:00:16.160
Write an expression for the area of the sector.
00:00:16.780 --> 00:00:22.110
We know that the expression for the area of a circle with radius π is ππ squared.
00:00:22.720 --> 00:00:27.140
And we know that angles around a point sum to 360 degrees.
00:00:27.860 --> 00:00:35.420
To find the fraction of the circle a sector with central angle π is, weβre going to divide π by 360.
00:00:35.670 --> 00:00:38.000
Itβs π over 360.
00:00:38.840 --> 00:00:42.240
Finally, we need to find an expression for the area of the sector.
00:00:42.690 --> 00:00:47.620
The fraction of the circle the sector is, is π over 360.
00:00:48.110 --> 00:00:55.000
So we need to find π over 360ths [360] of the total area of ππ squared.
00:00:55.580 --> 00:00:59.640
In maths, we commonly interchange βofβ and the multiplication symbol.
00:01:00.100 --> 00:01:09.140
So the expression for the area of the sector with central angle π is π over 360 multiplied by ππ squared.