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Current time:0:00Total duration:2:27

2003 AIME II problem 5 minor correction

Video transcript

I want to do a quick correction to the aim problem where we cut out a wedge of a log in that problem so we had a wedge so just to remind ourselves we had a log that looked like that we made one cut that was right along that was perpendicular to the axis of the log and we made another cut that hasn't had a 45 degree angle so it was like that and the solution to the problem had to figure out the volume of the wedge and the big trick there was so if I drew the wedge like this so let me take a side view of the wedge so this is a side of the wedge right over here I could shade it to show that it has it's kind of round so if I were to shade it you can kind of see that it is round so this is a side view of the wedge we knew that this right here is a 45 degree angle and the way that we solved the problem or the kind of trick was to say hey if we had another wedge like this we just stacked it on top of this one if we just flipped it over and made it like this then we also have a 45 degree angle over here and then we would make a cylinder and it's very easy it's very easy to figure out the height of a cylinder and I misspoke and I said it was lucky that we had a 45 degree angle because in the last video I was actually visualizing it incorrectly I said oh because if you had anything less than a 45 degree angle this wouldn't have worked out properly but I was wrong it would work out properly let me show you so if this lets say whatever whatever angle whatever angle you have here so this is going to be a 90 degrees over here whatever angle you have over here so let's call that theta this over here they have to add up to 180 so theta plus 90 plus this has to be 180 or theta plus this has to be 90 or this could be you just call this 90 minus theta now when you if I were to take the same thing if I took another kind of wedge like this and flipped it over over this thing it's not this angle that's going to be right here it's this angle so let me just draw it right over here so it would look like this it would look like this where this now is Theta this end right here is actually that end on the flipped version and now this angle right over here is now 90 minus theta so clearly you have 90 minus theta plus theta so this thing is going to be a right angle no matter what this no matter what obviously I has to be a reasonable angle but no matter assuming that it's less than 90 degrees it would have worked out you could have done the same trick anyway hopefully that clarifies it and I apologize for the incorrect visualization on the last video