00:01
I have here a diagram of the shelter with the cylindrical part down here on bottom, labeled with a height of 30 yards, and then the hemispherical roof up top here with a radius of 400 yards.
00:22
And below i've written everything else we know with the volume of a cylinder here, a volume of a sphere here, the conversion of yards to meters, and the amount of volume an air.
00:42
In order to find the volume of air when there are 150 people present in the shelter, we need to find the total volume of air without any people and subtract the volume of 150 people.
01:10
So our first step is going to be to make sure that we have the same units across the problem.
01:22
So right now we're working with yards for the radius and height of the shelter and meters cubed for the people, the volume of people.
01:33
But we're going to need to either convert meters cubed to yards cubed or yards to meters.
01:41
You could do it either way, but i'm going to convert yards into meters.
01:49
So in order to do that, we've got 400 yards for the yard.
02:03
That's equal to 0 .9144 meters.
02:10
So you can write that as 0 .9144 meters for every yard.
02:16
This way our unit of yard cancels out and we get 365 .76 meters for our radius of the shelter.
02:32
Then we can do the same thing for height.
02:38
We start with 30 yards for the height of the cylinder times 0 .9144 meters for each yard.
02:51
The yards cancel out and we're left with meters, specifically 27 .432.
03:02
And that is our height.
03:07
And now we can start thinking about the volume of the shelter.
03:11
The volume of the total shelter, we'll write that as volume total, is going to be equal to the volume of the cylinder plus half the volume of the sphere, where the radius is equal to r.
03:32
So using our equations here, we can start with the volume of the cylinder.
03:43
So that's going to be pi times the radius squared.
03:47
The radius here is 400 yards or 365 .76 meters, like we just calculated.
03:53
And that's going to be squared times the height, which is again like we just calculated, 27 .432 meters...