NeoPets Riddles (Lenny Conundrums) and Answers Here

But you do not know what is contained in the sphere. This is an egg, let's say the yoke causes eggs to sink and the white makes them float because it is less dense than the water..... the volume would be higher than 280000 because if that egg was to crack the total amount of fluid that would be in that tub would be whatever + 280000 + whatever was in the 28%. Plus do not say that there may have been air, who knows, the egg could have been slightly frozen too. I think you are overthinking this.

Do not confuse density with volume or mass.....

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edstock wrote:

I've been calculating volume and area using calculus and if I can figure out how to integrate (r^2 - y^2) ^ (1/2) dy (where r is a constant), then I'll be able to solve this one.

Hmm, I think I set up my integral wrong. I was using infinitesimal rings, but I was using cylindrical rings and I think I need to use infinitesimal truncated cones instead.

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Answer?
Simply think of it this way: 72%=280000 that means 1%=3889 so take the remaining percent, 28%, and 28% =108892 so add them together and you have 388892 cubic centimetres.

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Re: Answer?

gear50213 wrote:

Simply think of it this way: 72%=280000 that means 1%=3889 so take the remaining percent, 28%, and 28% =108892 so add them together and you have 388892 cubic centimetres.

Ah, but that assumes the volume is proportional to the area. Not a good assumption.

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Simply think of it this way: 72%=280000 that means 1%=3889 so take the remaining percent, 28%, and 28% =108892 so add them together and you have 388892 cubic centimetres.

That's if you round it to start with, because 1% is 3888.8889. So basically all you have to do is multiply it by 100% since you have 1% and that makes 100% = 388888.89 so rounded it's 388889.

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Re: Answer?

gear50213 wrote:

Simply think of it this way: 72%=280000 that means 1%=3889 so take the remaining percent, 28%, and 28% =108892 so add them together and you have 388892 cubic centimetres.

That's if you round it to start with, because 1% is 3888.8889. So basically all you have to do is multiply it by 100% since you have 1% and that makes 100% = 388888.89 so rounded it's 388889.

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Re: lenny

evilness wrote:

But it sounds like they are just trying to trick people, because 72% of the surface area of the egg was below the water line, then isn't 72% of the egg under water?
So then why isn't 280,000 cubic centimetres the part that's under the water?
So then wouldn't you just divid 280,000 by 72% then just multiply it by 100 to get the size of the egg?
Or did I miss something, which would not be the first time, and rounding the answer would make it ... 388,889.

You placed it in a tub of water and found that it displaced exactly 280,000 cubic centimetres. However, it was floating on the water, and only 72% of the surface area of the egg was below the water line.

I posted this back on page 709, I soooo hope I'm right. But I bet there is some other way to figure it out to make me wrong.

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evilness wrote:

Simply think of it this way: 72%=280000 that means 1%=3889 so take the remaining percent, 28%, and 28% =108892 so add them together and you have 388892 cubic centimetres.

That's if you round it to start with, because 1% is 3888.8889. So basically all you have to do is multiply it by 100% since you have 1% and that makes 100% = 388888.89 so rounded it's 388889.

Again, 72% of surface area NOT EQUALS to 72% of a volume....

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Okay, for anyone that wants to work at it, Ask Dr. Math at mathforum.org derives the integral for the surface area of a spherical cap.

I picked a value c as the distance from the center of the sphere straight up to the water line, then used his integral to find the area of the sphere that is under water. This is 72% of the total area, so I could then use the formula A = 4 * pi * r^2 for the total area to get c in terms of the radius r.

I used circular disks to create an integral for the volume of the sphere below the water line (integrating from -r to c). Substituting my formula for c and using that the underwater volume is 280,000 cc, I could calculate r^3 (or r if I want it). I then plug that into the spherical volume formula V = (4/3) * pi * r^3.

I'm not sharing my numerical answer, but as I stated before, I come up with about 85% of the volume of the sphere underwater.

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edstock wrote:

Okay, for anyone that wants to work at it, Ask Dr. Math at mathforum.org derives the integral for the surface area of a spherical cap.

I picked a value c as the distance from the center of the sphere straight up to the water line, then used his integral to find the area of the sphere that is under water. This is 72% of the total area, so I could then use the formula A = 4 * pi * r^2 for the total area to get c in terms of the radius r.

I used circular disks to create an integral for the volume of the sphere below the water line (integrating from -r to c). Substituting my formula for c and using that the underwater volume is 280,000 cc, I could calculate r^3 (or r if I want it). I then plug that into the spherical volume formula V = (4/3) * pi * r^3.

I'm not sharing my numerical answer, but as I stated before, I come up with about 85% of the volume of the sphere underwater.

Oh my.. The lenny now requires integrals to solve... I haven't seen a live integral since passing my Differential Equasions back in college, and that was a while ago.... If things go this way - we'll be messing with nuclear physic before long!

In the mean time I did a very rough brute force estimation and came up with about 88% of the volume being underwater. But my answer is too rough to consider, so I won't post it to avoid confusing anyone....

Anyway, I'm giving up on this one for now. Have to attend to other errands, so I'll stop here.... I doubt I'd be upgrading my trophy this time one way or another...

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The radius of the sphere was figured out on page 715 - I have double checked and it is correct; 45.29

So using the formula

Volume = 4/3 *pi*radius cubed
you get
V - 4/3 *3.14* (45.29)cubed
I get 388933

Any objections? I already posted the wrong answer Sad

so it doesn'tt matter to me, except to figure it out.

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Again, this person stated that we know 72% of the volume, WHICH WE DO NOT! We know that 72% of the surface area of the sphere is underwater, and that volume is 280,000 cc. That is NOT 72% of the volume.

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I'm sorry to sound stupid, but is the answer 388933 or 45.29?

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It WOULD be 388933, but that is both rounded AND figured incorrectly. I am not sure of a correct answer yet.

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neither.

I found this formula relating volume and surface area. Does it help? I have tried to work with it but am not sure I have enough or the right data

Volume = radius/3 * surface area

And yup when I look back on the other work relating to the radius I noted above, I figured out that error.

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oh, so no right answer yet?

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it looks easy but is pretty hard. im really getting confused on this one

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I get V = 346,232.985cc.

Google "spherical cap". The first entry should be Worlfram Mathworld.

If the cap represents 72% of the surface area, then
2*pi*R*h / 4*pi*R^2 = .72
Therefore,
h = 1.44R

Plug that into the volume formula for a spherical cap:
280000 = (1/3)*pi*h^2*(3*R-h)
and solve for R.

Plug R into the volume formula for a sphere.

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would the cap not be the portion above the water and if so should we use .28 instead of .72 in the first formula?

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Either portion can be considered a cap. 280,000cc corresponds to the larger cap (below water).

I misspelled Wolfram above.

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