ok, so go with my answer, TPH mistook I for a variable "I" and not absolute values. Or i shouldn't say mistook, it is I! there is an a symbol on your keyboard that you can use for absolute values. on US keyboards it is the same key as "\", just hold down "shift" while you're pressing that key and you get "|", which is the absolute value sign
The volume of a right-cylinder is given by , however, in this particular cone, . This is why Samantha made a distinction between the 's and used . realizing that the first is for the height, she decided not to differentiate that one. However, this is incorrect. Janvdl is right. if it is perfectly valid to treat the as in every way. in fact, this is a prevalent related rates technique. a lot of questions like this require you to solve for one variable in terms of another so you can differentiate a single variable function, we do not make distinctions between the same variable despite the fact it came from two different quantities.
even if your method was right Samantha, you would still get it wrong, why did you plug in 1 for the r that represents the height? if h is equal to r, then when r = 2, the height would be the same. and looking at it again, it seems you didn't differentiate at all. i'm sorry but what you did is confusing (i am looking at your last attempt at the question). can you explain exactly what you were doing so that we can clear up any misconceptions you have?
Yes, i did indeed use and i tried using implicit differentiation(like you taught me Jhevon!)
But then Samantha gave me this formula and i realised that h = r.