Mark Otto Posted May 21, 2002 Share Posted May 21, 2002 OK heres the problem....you have a spherical rubber balloon and you decrease the air inside by half while keeping the balloon in the shape of a sphere. How does the new radius compare to the old radius? Express your answer in lowest terms in fraction form. anyone? Link to comment Share on other sites More sharing options...
sp00nman Posted May 21, 2002 Share Posted May 21, 2002 I'm guessing that the radius = 2 thirds of the original radius, not 1/2. But that's just my first impression guess. Link to comment Share on other sites More sharing options...
lexor Posted May 21, 2002 Share Posted May 21, 2002 Isn't it 1:1 since the size of the baloon stays the same and since it's a sphere the radius stays constant? Link to comment Share on other sites More sharing options...
harry416 Posted May 21, 2002 Share Posted May 21, 2002 almost sounds like the related rate problems i encountered in calculus...*shudder*:bandit: Link to comment Share on other sites More sharing options...
aragorn73 Posted May 21, 2002 Share Posted May 21, 2002 42. :p Link to comment Share on other sites More sharing options...
Mark Otto Posted May 21, 2002 Author Share Posted May 21, 2002 no the sphere would change size as the air is let out to half of waht it was before....the radius therefore would change Link to comment Share on other sites More sharing options...
OrangesOfCourse Posted May 21, 2002 Share Posted May 21, 2002 tsk tsk tsk.. what has the world come to.. lol.. :D :p Do it your self anormal :p :D but we will always lub you man :) Link to comment Share on other sites More sharing options...
liar2 Posted May 21, 2002 Share Posted May 21, 2002 wouldn't the ratio still say 1:1? Link to comment Share on other sites More sharing options...
sp00nman Posted May 21, 2002 Share Posted May 21, 2002 Originally posted by lexor Isn't it 1:1 since the size of the baloon stays the same and since it's a sphere the radius stays constant? The balloon would shrink if you took out air, thus would the radius. The radius doesn't stay constant. The only thing that stays constant is pie (the math term, not the eating type). :) If you did a simple problem, perhaps: Volume Formula : Surface Area (I have these written down somewhere. I think I remember them but I don't want to throw it off. Check your math book) Just put in simple numbers, like 5... NOT 1 or 0. Work out the problem and find the radius ®. Then... 1/2Volume : Surface Area. Plug in everything the same for the original terms, but leave the radius as a variable. Work out the problem and find the variable. Link to comment Share on other sites More sharing options...
lexor Posted May 21, 2002 Share Posted May 21, 2002 ok it's hard to show the algebra in here, so I'll just tell you the answer. r1/r2 = 1/ sqrt 2 (sqrt = square root) Link to comment Share on other sites More sharing options...
mmaacckkoo Posted May 21, 2002 Share Posted May 21, 2002 I'm pretty sure the smaller radius is 1/(the square root of 2) the size of the larger radius. If you try it our with area that's what you get. If you just look up the formula for the volume sphere you can find out if I'm right. Link to comment Share on other sites More sharing options...
pHuzi0n Posted May 21, 2002 Share Posted May 21, 2002 Hehe... using the net to cheat on extra credit. All ya need is a bit of algebra and the equations for volume of a sphere... i don't feel like typing an explanation so the answer is R1=R2 - 2^(1/3) That's the best I can type it:roll: Link to comment Share on other sites More sharing options...
lexor Posted May 21, 2002 Share Posted May 21, 2002 I used the formula for the volume of a sphere and had V1 = 1/2 V2. Thus mmaacckkoo is right it does work out algebrarically with no numbers used! Link to comment Share on other sites More sharing options...
Mark Otto Posted May 21, 2002 Author Share Posted May 21, 2002 how do i get the cubic root of a number? say i have 65.5 = r^3 how do i simplify that? Link to comment Share on other sites More sharing options...
redrope Posted May 21, 2002 Share Posted May 21, 2002 Originally posted by aragorn73 42. :p Thats as good as mine. :p Link to comment Share on other sites More sharing options...
pHuzi0n Posted May 21, 2002 Share Posted May 21, 2002 Cubic root is expressed either as x^(1/3) or like square root but with the number 3 on the left sort of above the root sign... Link to comment Share on other sites More sharing options...
pHuzi0n Posted May 21, 2002 Share Posted May 21, 2002 Btw, isn't it wonderful how people forget everything they've learned in school ;) Link to comment Share on other sites More sharing options...
Ravager Posted May 21, 2002 Share Posted May 21, 2002 Area for sphere: 3/4*PI*r^3 = X Lets say big balloon has radius of 10 Area of sphere = 3/4*3.14*10^3 = 2355cm cubed You remove half air, so X = 1177.5 Let Y represent new radius So: 3/4*3.14*Y^3 = 1177.5 Now bring everything to one side 3/4*3.14*Y = 10.5598 3/4*Y = 3.363 Y = 4.48 cm so about 5 New radius is 1/2 of old radius Link to comment Share on other sites More sharing options...
lexor Posted May 21, 2002 Share Posted May 21, 2002 Anormal: there are no cubic roots in the volume of a sphere formula! it's: V1 = 4/3 * pi * r^2 V2 = 1/2 V1 = 2/3 * pi * r^2 rearrange for r and you get: r1/r2 = 1/ (square root 2) Link to comment Share on other sites More sharing options...
Ravager Posted May 21, 2002 Share Posted May 21, 2002 No, you've got that wrong lexor. There is a cube function is VOLUME of a sphere. U must be mixed up with surface area although that's not the correctly formula, there is a squared function in there. Link to comment Share on other sites More sharing options...
Mark Otto Posted May 21, 2002 Author Share Posted May 21, 2002 surface area = S S=(4)(pi)(r^2) for VOLUME, volume = V V=(4/3)(pi)(r^3) ;) Link to comment Share on other sites More sharing options...
pHuzi0n Posted May 21, 2002 Share Posted May 21, 2002 /me made a miscalculation... it's R1=R2*2^(1/3) Link to comment Share on other sites More sharing options...
Ravager Posted May 21, 2002 Share Posted May 21, 2002 Exactly what I said :) Follow my example Abnormal, I'm very sure it's right Link to comment Share on other sites More sharing options...
OrangesOfCourse Posted May 21, 2002 Share Posted May 21, 2002 Originally posted by Ravager Exactly what I said :) Follow my example Abnormal, I'm very sure it's right For the record.. its Anormal.. not Abnormal :p Link to comment Share on other sites More sharing options...
Ravager Posted May 21, 2002 Share Posted May 21, 2002 didnt notice! :o Link to comment Share on other sites More sharing options...
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