00:01
So for this problem we have a bacteria that has a diameter of two micrometers.
00:10
And we want to obtain its volume in cubic centimeters.
00:28
And we also want to obtain its surface area in square millimeters.
00:44
Now, consider, then we can consider this bacteria as spherical.
00:51
Now in that case, we will have that, the volume for this bacteria, since it is spherical, is 4 over 3 times pi times the radius to the cube, and the surface area is 4 pi times the radius square.
01:17
Now the first thing that we need to do is to obtain the radius because we are given the diameter of this bacteria.
01:26
Now we note that the radius is half of this diameter.
01:31
So in here, substituting that we will obtain that the radius is one micrometer.
01:41
Now in each case we need to transform this.
01:45
For example, in the case of the volume, we need to transform.
01:48
Into cubic centimeters.
01:52
And in the case of the surface area, we need to transform this quantity into a millimeter's square.
02:01
Now, we're going to try that first with the volume.
02:05
We know that that is 4 over 3 times pi the radius.
02:13
Now, i'm going to transform that quantity.
02:18
In here, so we will have one micrometer.
02:26
Now, to transform this first, we're going to transform this into meters and then from meters to centimeters.
02:38
Now, we know that in order to cancel the micrometers starting here, we need to put in the denominator how much this is in meters.
02:50
So we know that one meter is 10 to the 6 micrometers.
02:56
So we can eliminate this...