WEBVTT
00:00:01.110 --> 00:00:05.760
Find to the nearest tenth the total surface area of this cylinder.
00:00:07.700 --> 00:00:20.670
Finding the surface area of a cylinder looks like this: finding the area of the base, multiplying that by two, and then finding the area of the rectangle that’s formed between the two bases.
00:00:21.980 --> 00:00:24.450
The net of a cylinder looks like this.
00:00:26.330 --> 00:00:31.290
And we need to find the area of the two circle bases and then the rectangle from the middle.
00:00:32.790 --> 00:00:40.990
We first find the area of the circle and we multiply that by two because there’re two bases.
00:00:42.510 --> 00:00:45.020
And then we add the area of the rectangle.
00:00:47.150 --> 00:00:57.070
To find the area of the bases, which are circles, we use the formula for finding area of a circle, which is 𝜋 times the radius squared.
00:00:58.600 --> 00:01:03.240
And don’t forget to bring down your two because we have two circle pieces.
00:01:05.060 --> 00:01:10.300
And we find the area of a rectangle by multiplying base times height.
00:01:12.300 --> 00:01:22.410
You recognize right away that the height of this rectangle is 12 millimetres, but the base is not as intuitive.
00:01:23.980 --> 00:01:33.240
The base of the rectangle, or maybe even you would call it the length of the rectangle, is the distance around the circle.
00:01:34.780 --> 00:01:42.230
The circumference, the distance around this circle, is the length of our rectangle.
00:01:44.230 --> 00:01:47.750
And what it is the formula for finding the circumference of a circle?
00:01:49.360 --> 00:01:51.470
It’s 𝜋 times the diameter.
00:01:53.210 --> 00:01:55.720
Okay, now we have our full formula.
00:01:56.120 --> 00:02:05.420
Surface area of a cylinder looks like this: two times 𝜋𝑟 squared plus 𝜋 times the diameter times the height.
00:02:07.500 --> 00:02:09.170
Let’s start plugging in values.
00:02:10.730 --> 00:02:15.610
We’re given 16 millimetres, which is the diameter of the circle.
00:02:15.970 --> 00:02:20.560
But we need to know the radius; the radius is half of the diameter.
00:02:21.720 --> 00:02:24.610
The radius in this case would be eight millimetres.
00:02:25.840 --> 00:02:28.880
So we’ll plug in eight and then eight squared.
00:02:30.570 --> 00:02:36.810
We need the diameter to find the area of the rectangle portion, so we plug in 16 for the diameter.
00:02:37.770 --> 00:02:40.110
And the height of our cylinder is 12.
00:02:42.890 --> 00:03:02.190
The area of our circle base times two equals 402.12, the area of the rectangle portion 603.19, when I add those together, I get one 1005.31.
00:03:02.220 --> 00:03:12.240
But I remember that the question asked me to round to the nearest tenth, so I say 1005.3.
00:03:12.330 --> 00:03:18.470
And then I don’t forget my units, millimetres squared.
00:03:18.800 --> 00:03:25.110
The total surface area of this cylinder, 1005.3 millimetres squared.