NeoPets Riddles (Lenny Conundrums) and Answers Here

News is out, and so is a new LC.

Kauvara is making a special potion. For this particular potion, she's filling a bottle in the shape of a pentagonal pyramid: the base is a regular pentagon, 15cm to a side, and the height of the "pyramid" is 32cm. Assume these measurements are for the interior of the bottle.

Assume the flow of potion into the bottle starts at zero and increases at a rate of 1 millilitre per second per second. How many seconds will it take to completely fill the bottle? Please round to the nearest whole number.

I think the volume of a pentagonal pyramid is

(1/12)(a^2)h*sqrt(25+10*sqrt(5))
Where a is the side length of the pentagon base, and h is the height of the pyramid.

Ah, pure math. What a relief after the last 4 weeks. For an order of magnitude check, I got between 1 and 2 minutes. Anyone else?

Concur with the volume formula.

I got an answer between 1 and 2 minutes.

wow you all are fast. i used up a lot of time double-checking.
between 1 and 2 minutes, yes.

it was less than 20 seconds...O_o?

between 1 and 2 minutes is very illogical... accounting for the size of the container and the acceleration of the water into it...:/

1 mililiter does equal 1 cetemeter cubed...

Where is the dr/dt go?

it's actually very logical based on the volume of the pyramid.
anyway, 20 seconds would only fill 210 mL based on the problem

A bottle with less than 200 mililiters fills up in over a minute when it is filling at the acceleration specified...I think not.

1 sec 1 ml, 2 sec 3 ml, 3 sec 6ml, 4 sec 10ml...
...18 sec 171 ml...

whatever...I shall likely not be back on this board for another few months or so...I only come when whim brings me.

i wasn't even referring to 210 as the volume.

never mind...it would have to be 5000-10000 mililiters.:*

some how my calculations must have met a snag somewhere...

it seems odd that 28000 square centimeters can fit in a square foot.

Hi guys! I just want to know.. your last number is 1 or 2? I don't know wich will be the "nearest whole number"
Thanks

If is between 1 and 2, then you round down if it is less than 1.5 and up if it is greater than 1.5. I didn't get anything that was exactly .5 on the end, so you don't need to worry about which way to round that.

Is fishmonkey right with this pattern?
1 sec 1 ml, 2 sec 3 ml, 3 sec 6ml, 4 sec 10ml...18 sec 171 ml...

I don't think so. The rate of filling increases 1 ml/s^2. So after one second, the rate has gone from 0 ml/s to 1 ml/s. That turns into only 0.5 ml filled after one second. In the second second, the rate goes from 1 ml/s to 2 ml/s. That will fill another 1.5 ml for a total of 2 ml so far. In the third second, the rate goes from 2 ml/s to 3 ml/s, adding 2.5 ml for a total of 4.5 ml. So the pattern you are citing seems to be adding an extra 0.5 ml each second, causing the total to be (0.5) * t too high at the end of t seconds. Would lead to a time that is slightly too small, although probably by less than a second. Might lead to rounding in the wrong direction, however.

I got 8 seconds LOL