NeoPets Riddles (Lenny Conundrums) and Answers Here

What if it is the volume of the tank itself, not the volume it could possibly hold? I mean if the glass has a noticeable thickness than the “shell” of the tank would have a volume. The question asks “what is the volume of the tank in cubic metres?” it’s just an idea.

Very interesting. Something I had not actually considered. It appears that if I were asked the volume of a gas tank, I would answer how much gas the tank held. On the other hand, if I was asked what the volume was of the gas tank material, then I would give the answer for the shell.

To answer your question though,
Vexterior = 726.55365927581358467217354515671
Vinterior = 716.67947048211927207653509403511
Vshell = 9.874188793694312595638451121606 (or 9.8 cubic metres if submitted)

- PeckyP -

Another thought crosses my mind. While it could very well be a trick question, seeing as the question was given with an initial volume of what could be held, it seems logical to reply what volume the tank would hold given the restrictions used by the construction company.

- PeckyP -

P.S. For an evil lord, Sloth sure has problems if he can't even get a water tank made the way he wants. =P

so our final answer is 9.8?

wouldn't 9.87 be rounded to 9.9 ?

If you read the submission guideline in the question, you do not round up.


It's your call on what to answer. I answered 716.6 because I chose the volume of water the tank can hold. 9.8 is the volume of the material the tank is made from.

Kudos, very nicely done. For those that would like to look at the exact formulas, Wikipedia has a very nice article on icosahedrons: http://en.wikipedia.org/wiki/Icosahedron. Included in that is a very interesting shortcut statement: "When an icosahedron is inscribed in a sphere, it occupies less of the sphere's volume (60.54%) than a dodecahedron inscribed in the same sphere (66.49%)."

When I calculate the radius of the original sphere, subtract the 3 cm as PeckyP does, then recalculate the volume of the smaller sphere, I get 1183.691464 cubic meters. Multiplying this times 0.6054 (60.54%), I get a volume of 716.6068123 for the inscribed icosahedron. Due to the limit of only four significant digits on the percentage, I wouldn't want to trust that for my answer, but it certainly helps to make sure that the answer is in the right ballpark.

A very unique approach to the solution. It's certainly an easier concept to grasp to those without mathematical backgrounds. I never thought of inscribing an icosahedron into the unit sphere to come to this conclusion, but it is definitely quite intriguing.

- PeckyP -

I got the same answers as above. I submitted the volume that the container holds. The argument made earlier about water coolers and gas cans made earlier applies equally here. I have never heard anyone refer to the volume of a tank being anything other than how much material can fit inside of it. The only exception that I can think of would be cardboard boxes which are rated by the volume that they occupy, not what they hold. I am willing to bet the farm that the answer wanted is the volume the tank holds, and neither what volume it occupies nor the amount of material from which it is made. Good luck to all!

Hi all. i.got it correct. woohoo! The answer is 714.1. Only 46 got it.
The 3 cm is subtracted from the inradius, NOT circumradius. I just use the formulas from wolfram mathworld.

My steps:
- calculate sphere radius (outer icosaheron's circumradius equals this)
- calculate outer icosahedron's inradius
- calculate inner icosahedron's inradius (minus 3 cm from previous step)
- calculate inner icosahedron's volume
btw, i have the urge to make a pet named icosahedron. Unfortunately the name was taken

Oog, I hate maths =( Well, not really, 'cause math is one of the few consistencies in the world! But I hate these problems 'cause I get answers wrong based on using a formula that gives me a .1 margin of error and I round the wrong way and get the answer incorrect =(

Avoided looking at y'all's responses 'cause I didn't want to agonize the whole week over getting my math wrong ^^;

Of course it is. I made the assumption that the circumradius would decrease by the same amount, which is silly, considering that if that were to be true in general, the circumradius and the inradius would always be the same. When I went back and did the calculations by subtracting from the inradius instead of the circumradius, the circumradius actually decreased by more than 3.7 cm, which is about a 25% variation from what I used. I'm a little bit surprised the difference between the answers was only a little bit more than 2.5 cubic cm.

Ouch ! Hard one ^^"

This one makes no sense right now.

definitely not your usual word find puzzle.

This could be one where the letters need to be substituted with other letters to make sense? I just can't figure out what needs to be replaced with what

i'm trying to doing it like the sutek's tomb
but may be i'm wrong (and if i m right and you fin the question before me... just help my useless brain)

Not checked, so beware any errors

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