WEBVTT
00:00:00.870 --> 00:00:06.860
A right circular cone has a radius of three π₯ plus six and its height is three units less than its radius.
00:00:07.440 --> 00:00:18.190
Express the volume of the cone as a polynomial function, knowing that the volume of a cone with radius π and height β is π equals one third ππ squared β.
00:00:18.710 --> 00:00:26.960
So weβre told us that the radius was three π₯ plus six and our height is three less than the radius, which we can simplify.
00:00:27.400 --> 00:00:29.460
So β is equal to three π₯ plus three.
00:00:29.960 --> 00:00:39.030
So if the volume is equal to one-third ππ squared β, we can plug in three π₯ plus six for π and three π₯ plus three for β.
00:00:39.570 --> 00:00:46.490
Now since we have a one-third, that can cancel with the threes for the height, and this will make our work a little bit easier.
00:00:47.100 --> 00:00:54.200
So now we need to square three π₯ plus six, which is three π₯ plus six times three π₯ plus six.
00:00:54.200 --> 00:00:55.480
And now we need a foil.
00:00:57.240 --> 00:01:03.040
And when foiling that, it gives us nine π₯ squared plus 18π₯ plus 18π₯ plus 36.
00:01:03.040 --> 00:01:06.140
So letβs simplify that before we multiply by π₯ plus one.
00:01:06.820 --> 00:01:12.630
And we get π times nine π₯ squared plus 36π₯ plus 36 times π₯ plus one.
00:01:13.300 --> 00:01:14.220
Now letβs distribute.
00:01:14.800 --> 00:01:19.670
Distributing the nine π₯ squared to π₯ plus one, we get nine π₯ cubed plus nine π₯ squared.
00:01:20.190 --> 00:01:25.840
Distributing the 36π₯ to π₯ plus one, we get 36π₯ squared plus 36π₯.
00:01:26.340 --> 00:01:30.900
And distributing the 36 to the π₯ plus one, we get 36π₯ plus 36.
00:01:31.270 --> 00:01:33.030
Now we can combine like terms.
00:01:33.660 --> 00:01:41.960
Therefore, the volume is equal to π times nine π₯ cubed plus 45π₯ squared plus 72π₯ plus 36.