NeoPets Riddles (Lenny Conundrums) and Answers Here

bye!

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I think most of us have come up with the same answer on this one Smile

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Eww ; something can help me with the lenny ?
While strolling through Tyrannia one bright sunny day, you came across a Grarrl egg. It was a perfect sphere. 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.

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The answer is 388889
?

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Is not linear
We are talking about a sphere here, the volume is not linear as a cylinder.

It is a little more complicated than that.

The volume of a sphere is:

Vs = 4 * PI / 3 * r^3

In this case we know the 72% percent of the volume so...

280,000 = (0.72) * 4 * PI / 3 * r^3

then the sphere radius is 45.28

Now the volume of the segment outside of the water we got these 2 equations...

Vp = (PI/6) * (3 R^2 + h^2) * h

r = (h^2 + R^2)/(2 * h)

where...

the segment outside of the water has a circular base, the radius of that base is R, and the height of the segment is h.

So, we know 72% is inside the water, it is the same that saying 72% of the diameter is inside the water, or 28% of the diameter is outside the water.

diameter = 2 radius = 90.56

h = 90.56 * 0.28 = 25.3568

Now with "h" and "r" you can calculate "R"

R = 40.661

and with this you can calculate the volume of the segment

Volume of the segment is 74,389 cubic centimeters.

I hope I explained myself well Very Happy

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Flaw in our thinking
surface area does not equal volume.
Surface area = 4-pie(radius squared)
Volume = 4/3 times pie (radius cubed).

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We got different math results but our ideas are the same.

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klo wrote:

We got different math results but our ideas are the same.

Ok, I verified the result, but you never know, guys, made your calculations and submit the result you think is right.

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The sphere... it is... spherical - right?
So 72% of its surface area is NOT necesserily 72% of the volume...

If you imagine a submerged sphere:

Code:





     ,,,

--- /---\----

   |     |

    \   /

     '''

You can see that since it's more than half submerged, there would be a lot less of a surface area on top of the water than there is below... I can't quite put it in words... but it feels to me that 72% of surface area, should not be taken for 72% of volume.... Is anybody following me?

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lem wrote:

The sphere... it is... spherical - right?
So 72% of its surface area is NOT necesserily 72% of the volume...

If you imagine a submerged sphere:

Code:,,, --- /---\---- | | \ / '''

You can see that since it's more than half submerged, there would be a lot less of a surface area on top of the water than there is below... I can't quite put it in words... but it feels to me that 72% of surface area, should not be taken for 72% of volume.... Is anybody following me?

yes Lem, I am agreeing with ya

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I think the sphere concept throws people off, volume is still volume, whether it is a sphere or a cone, or a cube, it is still what it is. When they say 72% of the surface is under water, well, that is because 28% of the sphere is lighter than water.... if that sphere was completely under water it would be a different subject.

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I won 922 NP. But I didn't get in the top 250. Sad

Oh well. Maybe this time.
The new lenny conundrum is up. *waits for answer* I'm simply no good at it. lol

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lem wrote:

The sphere... it is... spherical - right?
So 72% of its surface area is NOT necesserily 72% of the volume...

If you imagine a submerged sphere:

You can see that since it's more than half submerged, there would be a lot less of a surface area on top of the water than there is below... I can't quite put it in words... but it feels to me that 72% of surface area, should not be taken for 72% of volume.... Is anybody following me?

Ahh. If you were to look onto a sphere head-on, you'd see a circle. If 72% of THAT circle was submerged, then 72% of the volume would be submerged. However, it is SURFACE AREA! So, how would it be figured?

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i just set it up like a ratio 72/280000 * 28/x and do the cross multiply and divide to find the remainder, 280000*28=7840000 then divide that by 72 to find x, which equals 108888.8888etc. and add that to the 280000 u already displaced because that is what the remaing 28 % of the egg would displace and u have the total (100%) displacement of the egg which is 388888.888etc and is rounded up to 388889cm^3, i hope that kind of helps i know other ppl have explained it this is just what works for me, if i confuse anyone i am really sorry

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I am also inclined to agree that 72% of the surface area DOES NOT equate to 72% of the volume.

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72% of surface area under the water definitely does not mean 72% of the volume under water.

On a side note, the mass of the egg is 280kg, the same as the mass of the displaced water. This, however, tells us nothing about the volume of the egg. Depending on the density, we could have eggs that are 10%, 50% or 90% under water with the same mass.

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.

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edstock wrote:

72% of surface area under the water definitely does not mean 72% of the volume under water.

On a side note, the mass of the egg is 280kg, the same as the mass of the displaced water. This, however, tells us nothing about the volume of the egg. Depending on the density, we could have eggs that are 10%, 50% or 90% under water with the same mass.

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.

Mass? No, the volume of the displaced water is the volume of the displacing matter. Therefore, the volume of the amount of the sphere UNDER WATER is 280,000 cc. The problem is finding the relation between surface area and volume. On a perfect sphere, if 72% of the SA is underwater, what percentage of the volume is under water?

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Qae wrote:

edstock wrote:
72% of surface area under the water definitely does not mean 72% of the volume under water.

On a side note, the mass of the egg is 280kg, the same as the mass of the displaced water. This, however, tells us nothing about the volume of the egg. Depending on the density, we could have eggs that are 10%, 50% or 90% under water with the same mass.

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.

Mass? No, the volume of the displaced water is the volume of the displacing matter. Therefore, the volume of the amount of the sphere UNDER WATER is 280,000 cc. The problem is finding the relation between surface area and volume. On a perfect sphere, if 72% of the SA is underwater, what percentage of the volume is under water?

Right, the volume under water is 280,000 cc, but the mass of the total egg is the same as the mass of the displaced water (at 1 cc = 1 g), so the mass of the egg is 280,000 g or 280 kg. The reason I mentioned it is that several pages back, people were trying to use the mass displacement to calculate the volume and it really has no relationship.

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Qae wrote:

On a perfect sphere, if 72% of the SA is underwater, what percentage of the volume is under water?

Absolutely, exactly the key question. And I think the answer is in the neighborhood of 85%.

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math
this is so not my game xD I really want that avatar, but I hate math, riddles, and puzzles. I should call up my math teacher.

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