00:01
First take note of a corresponding pair of sides, like 27 and 6.
00:08
If we want the volume ratio of the larger to the smaller one, then it would be 27 to 6.
00:15
Or if you compare 27 to 6, it's 4 .5.
00:19
Also, if you would have compared 18 to 4 ,4, you get 4 .5.
00:22
So 4 .5 is the scale factor larger to smaller.
00:27
The surface area ratio is going to be the scale factor squared, and 4 .5 squared is 20 .25.
00:43
If you want this as a ratio, 4 .5 is 9 halves, and then this squared would be 81 fourths, 9 squared over 2 squared.
00:59
And the volume ratio would be the scale factor cube, because volume is cubic units.
01:07
And 9 cubed is 729, and 2 cubed is 8.
01:21
So the volume of solid a is 28 cubic meters, and the volume of solid b is 1792 cubic meters.
01:29
If the solids are similar, what's the ratio of the surface area of a to b? well, if the volume to volume is 28 to 1792 a to b, first we can check to see if we can reduce this, 28 over 1792 is 1 over 64.
01:57
That's the ratio of the volumes.
02:04
But we want to go to the surface area, which is the squared units.
02:08
So let's take the cube root of this to get back down to the linear part for just the regular scale factor.
02:18
The cube root of 1 is 1 and the cube root of 64 is 4.
02:27
So that's the scale factor.
02:33
And now if we want the ratio of the surface areas, we'll then square this to get 1 squared as 1, 4 squared as 16...