Split (1)

train · 116k rows

role stringclasses 2 values	content stringlengths 0 2.1k	session_id int64 10 21.7k	sequence_id int64 0 2.38k	annotations listlengths 0 8
volunteer	the height and the radius.	8,595	961	[]
volunteer	And once we get that, we'll have, we'll be able to solve this problem.	8,595	962	[]
volunteer	because again, the radius is changing	8,595	963	[]
volunteer	and	8,595	964	[]
volunteer	what we can say is	8,595	965	[]
volunteer	1/2	8,595	966	[]
volunteer	is equal to	8,595	967	[]
volunteer	R over H	8,595	968	[]
volunteer	I'm gonna write this down right here.	8,595	969	[]
volunteer	You'll kind of see what I'm talking about.	8,595	970	[]
volunteer	So if I, I'm not gonna destroy your nice drawing, but	8,595	971	[]
volunteer	if I have a side view,	8,595	972	[]
volunteer	of this cone	8,595	973	[]
volunteer	we know that the radios up the top is one.	8,595	974	[]
volunteer	when the height is	8,595	975	[]
volunteer	2	8,595	976	[]
volunteer	But when we're at another	8,595	977	[]
volunteer	height,	8,595	978	[]
volunteer	the radius is something else.	8,595	979	[]
volunteer	when the height is	8,595	980	[]
volunteer	say 1.5	8,595	981	[]
student	Mhm	8,595	982	[]
volunteer	So it's a little bit of a proportion.	8,595	983	[]
volunteer	Um.	8,595	984	[]
volunteer	the radius to the height is always R over H and because	8,595	985	[]
volunteer	we have	8,595	986	[]
volunteer	kind of similar triangles working out. We can always say that the radius to the height	8,595	987	[]
volunteer	will always be 1/2.	8,595	988	[]
student	You said the radius would always be 1/2.	8,595	989	[]
volunteer	The radius to the height, the ratio of the radius to the height will always be 1/2.	8,595	990	[]
volunteer	So if you look at the, if you look at the big triangle	8,595	991	[]
student	Mhm	8,595	992	[]
volunteer	or the, the big triangle, the whole cone looked at from the side.	8,595	993	[]
student	Mm	8,595	994	[]
volunteer	We know that the radius is one	8,595	995	[]
volunteer	over the height is 2.	8,595	996	[]
volunteer	If you look at	8,595	997	[]
student	Mm	8,595	998	[]
volunteer	when the water's lower, the radius is going to be something else.	8,595	999	[]
student	Mhm.	8,595	1,000	[]
volunteer	and the height is gonna be something else, but they're always	8,595	1,001	[]
volunteer	they're always gonna be in proportion of 1 to 2, because they're corresponding parts of similar triangles.	8,595	1,002	[]
volunteer	Do you see what I'm saying	8,595	1,003	[]
student	Yeah	8,595	1,004	[]
volunteer	So, if you look at, look at the whole big triangle, which is the cone looked at from the side.	8,595	1,005	[]
volunteer	The radius is one and the height is 2.	8,595	1,006	[]
volunteer	When we look at	8,595	1,007	[]
volunteer	when the water's lower	8,595	1,008	[]
volunteer	the radius is gonna be something smaller, and the height's gonna be something smaller, but they'll be in proportion of 1 to 2 because they're	8,595	1,009	[]
volunteer	it's a similar triangle to the one that's	8,595	1,010	[]
volunteer	the big one	8,595	1,011	[]
student	OK	8,595	1,012	[]
volunteer	Do you kind of see what I'm saying	8,595	1,013	[]
student	Yup	8,595	1,014	[]
volunteer	So if you believe in your geometry, which you	8,595	1,015	[]
volunteer	I'm sure you had at some point. We know that corresponding parts of similar triangles are in proportion.	8,595	1,016	[]
volunteer	So	8,595	1,017	[]
volunteer	because we look looking at the side, we can see that	8,595	1,018	[]
volunteer	the small triangle when the water is lower	8,595	1,019	[]
volunteer	is a similar triangle to the big	8,595	1,020	[]
volunteer	cones	8,595	1,021	[]
volunteer	triangle, the, the when it's filled up with water, and the ROH will always be 1/2 in this case.	8,595	1,022	[]
student	Mm	8,595	1,023	[]
volunteer	So that is the trick to making beer this whole thing work because if we didn't know how the radius changed.	8,595	1,024	[]
volunteer	with respect to the height, we'd be missing a critical bit of information.	8,595	1,025	[]
volunteer	So what we really want to do	8,595	1,026	[]
volunteer	just bear with me a little bit more here before we, we're ready to solve this.	8,595	1,027	[]
volunteer	We can solve for our	8,595	1,028	[]
student	I think ours is like 14.	8,595	1,029	[]
volunteer	so 2R	8,595	1,030	[]
student	1/4	8,595	1,031	[]
volunteer	hold on a sec. 2 R equals H.	8,595	1,032	[]
volunteer	So an R is	8,595	1,033	[]
volunteer	H over 2, right? Oh, we don't want to sour our, we want to sulfur H, so.	8,595	1,034	[]
student	Yeah, 1 is over 8	8,595	1,035	[]
volunteer	So H is 2R.	8,595	1,036	[]
volunteer	The height is always 2 times the radius.	8,595	1,037	[]
volunteer	but R is alwaysh over 2 as well.	8,595	1,038	[]
volunteer	So if we substitute H over 2 into our formula for volume.	8,595	1,039	[]
volunteer	You're right, you	8,595	1,040	[]
volunteer	will get one, like a 1/4th factor. So what we wanna do is we want to take H over 2 and plug it in for RR.	8,595	1,041	[]
volunteer	So we get volume equals 1/3	8,595	1,042	[]
volunteer	I.	8,595	1,043	[]
volunteer	H/2^2 will be H^2 over 4, right?	8,595	1,044	[]
student	I think before like plugging stuff in, we need to like differentiate it and then we can plug it in at the end.	8,595	1,045	[]
volunteer	Um	8,595	1,046	[]
volunteer	well, you only want to differentiate with respect to 1 to 1 variable. You don't want to have two of them like R and H, OK?	8,595	1,047	[]
volunteer	You	8,595	1,048	[]
student	OK	8,595	1,049	[]
volunteer	you see what I'm saying	8,595	1,050	[]
volunteer	I'm gonna let you write this out cause I'm not doing very well	8,595	1,051	[]
volunteer	So what I would	8,595	1,052	[]
student	Mm.	8,595	1,053	[]
volunteer	what I would like if you would do for us and then you can	8,595	1,054	[]
volunteer	continue and finish the problem, which won't be too bad.	8,595	1,055	[]
volunteer	is what we want to do is we want to say,	8,595	1,056	[]
volunteer	V equals 1/3 pi R2H, but instead of R, we want to put H over 2 in there.	8,595	1,057	[]
student	Well, you said to do what, like B equals 1/3 pi.	8,595	1,058	[]
volunteer	So	8,595	1,059	[]
student	instead of R, we put	8,595	1,060	[]

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