00:01
So in this problem, i'm given a little rectangular prism and a bigger rectangular prism.
00:08
So as i have the smaller rectangular prism with side lengths 2, 3, and 2.
00:13
So 2 units tall, 3 units wide, 2 units deep or something.
00:17
This larger prism is similar to this right rectangular prism by a scale factor of 2.
00:25
We want to sketch both of these and compare their surface areas.
00:29
So we're going to be finding their surface areas and their volumes.
00:36
So when two figures are similar by a certain scale factor, that means all of the side lengths of this bigger shape, this bigger prism are proportional to the side lengths of this smaller prism.
00:52
And since it says i have a scale factor of two, that means all the corresponding side lengths of this prism are going to be exactly two times.
00:59
The side lengths of this smaller prism.
01:02
So this bigger prism, if this side length on the smaller prism was two, this side length is four, this side length is six, and this side length is four, because they are all doubled.
01:12
Okay.
01:13
So now let's find the surface area of each of these shapes.
01:18
So finding the surface area of the smaller shape, let's do this in green.
01:25
So i need to find the area of this face multiplied by two because there are two.
01:29
Of them.
01:30
The area of this face multiplied by two because there are two of them.
01:35
And the area of this face multiplied by two because there are two of them.
01:38
So the area of this first face is two times three, which is six, and there are going to be two of those faces.
01:46
I need to add the area of this face, which is going to be three by two, which is six.
01:55
Okay, and there are two of those faces.
01:57
I need to add up the area of this face, which is two times two, which is four.
02:02
And i need to multiply that by two because there are two faces.
02:06
So two times six is 12.
02:09
Two times six is 12.
02:11
Two times four is eight.
02:12
Adding those all together, i get a surface area of 32.
02:18
Okay, now let's do, say, in red, the surface area of the larger shape.
02:23
So i need to find the area of this face multiplied by two, the area of this face multiplied by 2 and the area of this face multiplied.
02:32
So the area of this face is going to be 24, four times six, and i need to multiply that by 2.
02:40
I need to take the area of this face, which is also 4 by 6, which is 24, and i need to multiply that by 2.
02:48
And then i need to add the area of this face multiplied by 2.
02:51
The area of that face is 16, and i need to multiply that by 2 as well.
02:58
This is all for surface area, not for volume.
03:01
My apologies...