Honors Geometry Extra Credit Help!


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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?

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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 :)

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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.

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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.

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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:

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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

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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)

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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.

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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

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