00:03
So this problem is about a restaurant that contains a partially filled fish tank.
00:08
It's a right circular cylinder with a diameter of 5 feet and a height of 6 feet.
00:13
So that's what i've drawn on the screen.
00:15
The manager wants to add a solid rock -like sculpture to the tank.
00:19
If the average weight of the material from which the sculpture is made is 4 pounds per cubic foot, and the manager's sculpture weighs 9 .8 pounds by approximately how much will the height of the water in the tank increase when the sculpture is fully subculture? merged.
00:34
Well, first let me fix this mistake here.
00:37
9 .8 pounds.
00:40
So for every cubic foot, it requires four pounds.
00:47
So, and we know that the total of the sculpture is 9 .8 pounds.
00:51
So the first step here is going to be to divide those two numbers.
00:55
Divide 9 .8 by 4.
00:59
And you get 2 .4 feet, 2 .45.
01:04
And that measurement is cubic feet.
01:09
Like that is the volume here of this item.
01:13
And that's important to know because the volume of the tank, the cylindrical tank here, has the formula pi r squared times the height.
01:28
So if we're looking for the height change, we need to know the volume being put in compared to some of the numbers in this volume formula.
01:37
So what i'm going to do is find the radius.
01:39
Since the diameter is 5 feet, the radius is 2 .5 feet.
01:44
I just cut that in half.
01:51
So if i plug that in, i have pi times 2 .5 squared.
01:58
And i know the height here.
02:00
I know the height is 6 feet, but i'm not really interested in the total volume of this cylinder.
02:06
I'm interested in the volume change in the cylinder.
02:10
So there's already some water in this fish tank and i'm looking for the height that changes once that sculpture is added in.
02:21
So that's that height that i actually care about here.
02:24
So h, we're just going to leave alone...