00:01
So in this problem, we are shown the top of a pool that a landscape architect is designing, and we are asked how much water will be needed to fill this pool four feet deep.
00:13
So what i need to find here is the volume by finding the area of the base here.
00:19
So the area of this whole base times the height of the prism, which would be four feet.
00:26
So to find the area of the space, i'm going to split this into two shapes.
00:31
Down here i'm going to do 11 times 1 .5, which is 16 .5 feet squared.
00:41
And up here, i'm going to use the formula for area of a trapezoid, which is one half of the height times base 1 plus base 2.
00:53
So that would be 1 half of the height, which is going to be 12 minus 1 .5, which is 10 .5, times base 1 plus base 2, which is 9 plus 11.
01:12
So that would give me 20.
01:18
So that's going to be 10 times 10 .5 when you reduce that, which is 105.
01:25
So if i add that to the 16 .5 feet squared, i get 121 .5 feet squared, which i'm going to go ahead and plug in for area of the base.
01:44
Times the height, which is 4, which gives us 486 feet cubed of water.
02:00
Now for b, it says before filling up the pool, it gets lined with a plastic liner...