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Ceoddyn

Simple Volume Question

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I took a very important test which contained something along the lines of the following question: A point C is 6 inches from plane M. Find the portion of volume that contains all points in between point C and plane M at most 12 inches from point C. I read it to mean the following: However, the only way I could get a correct answer out of the multiple choices (5 of them!), I had to make the 12 inches start on plane M just below point C (so the 12 inches is a leg and not the hypotenuse). Basically what I'm asking is, did anyone else take this very important test and find this error, or did I infact make the error?

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Do you know what the answers were?
I belive you should be able to do it this way, as it does seem like a cone really:
radius of base = sqrt(12*12+6*6)
= sqrt(108)
volume of cone = 1/3*6*(pi*r*r)
= 1/3*6*108pi
= 216pi

Maybe this isn't what you want but that's how it appeared to me. Hope it helps.

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Firstly, I think this is non-game related and therefore is disallowed on this forum.

But while we are at it anyway, I don't think this figure should be a cone at all. For example, consider the point in your diagram where the text "12" is written, that point is also between C and plane of M and lies within 12 inches of C. Therefore, to me it looks more like a hemisphere with center at C with a radius of 12 inches, cut off by the plane M, and basically you have to find the volume of the remaining portion.

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Definitely not allowed on the forum [smile]

Anyway, finding the volume of a cone would be way too easy. Why would they go through the trouble of defining a plane M if they could just as easily have said "find the volume of a cone with such and such properties"? Also, whenever you see the phrase "at most X units away from some point P", that's a dead giveaway you're dealing with a spherical shape. I'd say this problem was meant to test your ability to integrate an area with respect to one of its variables to determine a volume, subject to a constraint that determines the integration bounds.

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