WEBVTT
00:00:01.260 --> 00:00:06.020
Work out the area of the quarter circle, giving your answer in terms of π.
00:00:07.010 --> 00:00:20.080
Remember, the formula for area of a circular sector is given by a half multiplied by π squared multiplied by π, where π is the radius of the sector and π is the angle in radians.
00:00:20.760 --> 00:00:25.810
We can see that our quarter circle has a radius of three units and a right angle.
00:00:25.890 --> 00:00:28.300
Remember, thatβs just an angle of 90 degrees.
00:00:28.740 --> 00:00:30.940
We need this angle to be in radians.
00:00:31.080 --> 00:00:33.870
So how do we convert from degrees to radians?
00:00:34.470 --> 00:00:40.930
Well, we begin by recalling the fact that a full term, 360 degrees, is equal to two π radians.
00:00:41.190 --> 00:00:43.740
And then at this point, we have two options.
00:00:44.290 --> 00:00:49.880
We could find the value of one degree by dividing both sides of this equation by 360.
00:00:50.170 --> 00:00:54.380
So one degree is equal to two π over 360 radians.
00:00:54.850 --> 00:00:58.220
This simplifies to π over 180 radians.
00:00:58.360 --> 00:01:04.280
And we can therefore change from degrees to radians by multiplying by π over 180.
00:01:04.860 --> 00:01:15.740
Alternatively, and this method works nicely when the angle is a factor of 360, we spot that 90 degrees is a quarter of 360 as specified in the question.
00:01:15.980 --> 00:01:18.590
And we can divide both sides of the equation by four.
00:01:19.180 --> 00:01:23.880
Doing so, we can see that 90 degrees is equal to two π over four radians.
00:01:24.330 --> 00:01:26.510
That simplifies to π over two.
00:01:27.100 --> 00:01:33.010
Now that we know the size of the angle in radians, we can substitute everything into the formula of area of a sector.
00:01:33.350 --> 00:01:38.170
Doing so, we get a half multiplied by three squared multiplied by π over two.
00:01:38.660 --> 00:01:40.090
Three squared is nine.
00:01:40.090 --> 00:01:42.270
And we can write this as nine over one.
00:01:42.410 --> 00:01:44.560
So we can multiply these three fractions.
00:01:45.020 --> 00:01:47.080
We begin by multiplying the numerators.
00:01:47.080 --> 00:01:50.620
One multiplied by nine multiplied by π is nine π.
00:01:51.280 --> 00:01:53.120
And we then multiply the denominators.
00:01:53.150 --> 00:01:56.540
Two multiplied by one multiplied by two is four.
00:01:57.420 --> 00:02:02.490
And we see that the area of our sector is nine π over four units squared.