00:01
Okay, so we have another related rate problem where...
00:06
Oh, the answer has to be in home number.
00:10
Okay.
00:11
Sand is leaking out from a hole in a container and it forms a conical pile.
00:17
So, we assume the pile looks something like this, like a cone.
00:27
Look, if you want a cone.
00:32
Okay, tonical pile.
00:35
And the cone has to face that way, you know, because of gravity.
00:39
Height altitude is the same as radius so i didn't draw it perfectly because the radius has to be the same as the altitude which is the height and clearly that's not the case here but we'll just say r equals h so it's a wider pile than it looks the length of the pile or if the high of the pile is increasing at the rate of nine inch per minute so you're given the hd t equals nine find the rate at which the sand is leaking when the height is 12 inches.
01:15
So we're finding cubic inches per minute.
01:22
So we're finding dvdt, the rate of the sand leaking, so the volume of the sand that's leaking out the rate of that.
01:31
When the height is 12 inches.
01:34
So find dvd when h equals 12.
01:37
Okay, so first we need the volume of a cone because the shape of this pile is the cone.
01:45
So volume of a cone is 1 3rd pi r squared times height.
01:50
But we also know that radius equals height and because everything we're given is height, we're given that the height is 12, the hdt is easier to leave this equation in terms of h instead of in terms of r.
02:05
So we want to get rid of this r.
02:08
So since r equals h, when i see the r, i'm just going to plug in h.
02:14
So this equation turns into 1 3rd pi h to the 3rd.
02:20
And then because we're finding dvd -t, we want to take the derivative of v...