Math People!! (READ: TANGIE)

[tman]

I've got this worksheet for calculus. Theres a problem on it noone can solve, not even the teacher. Theres Extra credit involved for solving it. Whoever helps will be mentioned to 30 high school students, so thats your prize. Be jealous

-----Problem------

If the cylinder of largest possible volume is inscribed in a given sphere, the ratio of the volume of the sphere to that of the cylinder is:

a) sqrt(3) : 1
b) sqrt(3) : 3
c) 3 : 1
d) 2*sqrt(3) : 3
e) 3*sqrt(3) : 4

--------end problem-------

Help is appreciated, and I can't just take the 20% chance of guessing correctly, I must be able to explain it. Thanks.

[beef_bourito]

i got something that wasn't on the list, and i got it a few times.

vc=volume of the cylender
vs=volume of the sphere

i got vc = vs * 3/2^(5/2)

because:

the biggest rectangle you can fit in a circle is a square, if you need the proof i could probably cook it up for you pretty quickly, therefore:
diameter = height
2r=h

since vc=(pi)(r squared)h
then vc=(pi)(r squared)(2r)
vc=2(pi)(r cubed)

now using pythagorean theorem you find that the diameter of the sphere squared is equal to twice the diameter of the cylender squared:

allow the radius of the sphere to be known as x and the height of the cylender to be known as y

x squared = (2r) squared + (2r) squared

HA i just found the little hat thing, this will go alot faster

(2x)^2 = y^2 + y^2
(2x)^2 = 2y^2
4x^2 = 2y^2
x^2 = y^2/2
x = y/(sqrt 2)

vs = 4/3 (pi)x^3
vs = 4/3 (pi) (y/sqrt2)^3

y = 2r

vs = (4/3) (pi) (2r/sqrt2)^3
vs = (4/3) (pi) ((sqrt2)r)^3
vs = (4/3) (pi) sqrt(2^3) r^3
r^3 = 3vs/(4(pi) * sqrt(2^3))

vc = 2 (pi) r^3
r^3 = vc/(2(pi))

r^3 = r^3

3vs/(4(pi) * sqrt(2^3)) = vc/(2pi)
vc = 3vs*(2(pi))/(4(pi) * sqrt(2^3))
the 2 (pi)'s cancel
vc = 3vs/2*sqrt(2^3)
vc = vs * 3/2^(5/2)


I probably made a mistake somewhere along the line, if you find it tell me, i'd like to know. to read it easier you might want to write it out on paper in normal math writing, not this word processor math writing. if you have questions you can ask me.

if this helps, tell your class it was a 17 year old canadian named Luc.

[Gohan Ryu]

i love lamp.

[Damien]

LOUD NOISES!!!

sorry, I'm really really good at math but with a passion, I despise it. Unless it involves fun physics.

[beef_bourito]

Originally Posted by Gohan_Ryu

i love lamp.

and that's why you aren't going to university haha jk.

actually we just stated something similar to this in calculus class so it's good timing.

edit: i enjoy math and physics... actually sciences in general, the only reason im not taking biology this year is because it would be more work in a course that i in no way need for mechanical, aerospace or automotive engineering.

[tman]

i got lost halfway through your stuff, but i reasoned that the ratio of sphere to cylinder should equal the ratio of circle to square, and used 2 as a side of the square, giving a diagonal of 2.8, as well as a diameter of 2.8. using area formulas my ratio came to 6.2 : 4. answer a is 6.9 to 4 and e is 5.9 to 4, so I'd guess E. thanks!

[quteasabutton]

Originally Posted by Gohan Ryu

i love lamp.

my thoughts exactly. the last time i was good at math was somewhere around 8th grade or freshman year. after that, it all just went downhill. i'm not even taking math as a senior cuz it was killing my GPA. for some reason i thought physics would be a better idea.. sorry i can't help you with your calculus. "when i doubt...go with C" one guy i go to school with tested that theory, and on a scantron sheet picked C for every question on this huge test and actually passed.

[Vitamin J]

i hate maths

[beef_bourito]

if you reason that the volume of sphere to cylender will be the same as area of circle to square then:

area of square=x^2
area of circle=(pi)r^2

diameter = sqrt2 * x (pythagorean theorem)
r = x/sqrt2

area of circle = (pi)(x/sqrt2)^2
area = (pi) * x^2/2
(area*2)/(pi) = x^2

area of square = x^2
area of square = (area of circle * 2)/(pi)

ratio:
1:2/pi

[Damien]

its, "when in doubt, charlie out"

yes, it's true. i spent a day in probably each of my classes in college discussing this. teachers actually admitted to setting most answers at C. there's actually an explanation with how people think. C, normally being the middle answer has to do with people bring undecisive and not leaning towards either way. Although, with that, when a question has a answer "All of the above" or "none of the above", it is normally one of those especially pending on how few of those questions are. The less of those, the higher the probability of the answer being "all/none of the above." Also...darn. i waited to long to type it and now i forgot.

[tman]

but thats nowhere close to the answer choices, i realize i made up a number, but it sort of works

[beef_bourito]

and you shouldn't use specific measurements for these types of things because then it's only case specific. if you use variables it's a general statement that is true for all similar questions. like the area of a square is x^2 rather than the area of the square 2X2 is 4.

[beef_bourito]

yeah but your teacher will ask you to describe how you got it, and i don't believe that's any way to get those answers. i hate to say it but i think you're wrong, i'm not all that right either because i probably made a mistake somewhere along the line. ill run it by some of the koreans at my school, they're usually pretty good at this kind of thing.

[quteasabutton]

Originally Posted by Damien

its, "when in doubt, charlie out"

yes, it's true. i spent a day in probably each of my classes in college discussing this. teachers actually admitted to setting most answers at C. there's actually an explanation with how people think. C, normally being the middle answer has to do with people bring undecisive and not leaning towards either way. Although, with that, when a question has a answer "All of the above" or "none of the above", it is normally one of those especially pending on how few of those questions are. The less of those, the higher the probability of the answer being "all/none of the above." Also...darn. i waited to long to type it and now i forgot.

but then you have those teachers who make 3 correct answers and one seemingly correct answer that was worded poorly to possibly be interpreted as right but in all actuality is wrong and then have in addition an all of the above, none of the above, some of the above, and your mom goes to college as answer choices. so that way you're 99% likely to get it wrong.

i hated that teacher, still do. it was an AP econ class so it was all about theory and interpretation and the only way to get anything right was to be the kid who sat next to me or be the teacher himself. in short, i failed miserably. so all of the above isn't always the safest answer.

[Damien]

you can hate it all you want, but im right. ive done quite a few research and interviewed a 20 teahcers. 10 at UCF and 10 at a high school.

although it's not extensive, my memory serves as well and past tests that i still have from 7th grade...presents a lot of evidence. yes, if the test requires you to explain how you arrived at the answer then youre screwed, but that's not always the case. also, if the teacher asks later on, well, it's not your problem you guessed, they maybe disappointed, but oh well.

EDIT: I never said "all of the above" is always the correct choice. It also depends on how many of the question have that choice for an answer.