Never mind...i'm a dork...yeah, V=4.68...not enough ice to fill it...
Well...I just sent an email to the Neopets team asking if it is, in fact, a mistake. Whether or not I will receive an answer...I do not know.
I got a volume for the sphere of 4.19 m^3
the volume of the sphere = 4/3 * pi * r^3
so if the diameter is 2 m than the radius is 1 m
so 4/3 * 3.14 * 1^3 = 4.19 m^3 so I said that it would never be filled
Maybe they meant that the radius was 2 meters....*shrug*
Here's what I got, tell me if it makes ANY sense (probably not, haha)
ok:
I got
A volume of 4,19 for the sphere of ice
A volume of 4,68 for the tub
If it takes 1 minute for 1,5mm of depth or whatever to be melted off the ice, we would devide 4,19m/1,5mm (which would be 0.0015m)
I got an answer of 2793minutes.
It kinda makes sense. Imagine a 2m diameter sphere, pretty big eh? then imagine 1,5mm... pretty small. so it'll take a LONG time for it to melt.
Does ANY of this make sense?
but yeah, the tub really won't be COMPLETELY filled... but that's how long it should take...if i'm right... for the ice to melt completely...
ok.. now i see where 667 comes from.
I agree that it would take 2793 minutes to melt the ice ball. But, since the question asks how long would it take the tub to be filled, it would be longer than 2793 minutes to fill the tub. I set up an equation (4.1888m3/2793min = 4.677m3/Xmin) and solved for X. So, to fill the tub, it would take 3118 (3117.996) minutes to fill the tub completely. Of course, this time would mean that the ice ball would have to be larger than that which is provided... Hmm.
I hope my math is right... Check it before you do anything.
It shouldn't take 2793 minutes to melt the ice ball, because it melts equally all around the ball. Think about it: It doesn't melt only from the top down, it melts all around because the question says "if it melts the surface of the ice uniformly". As such, even though the diameter is 2m, since every spot on the sphere's surface melts at once, you really only need to measure how long it would take to melt the radius, and the volume only matters to determine how much water is in the sphere to compare it to the amount of space in the tub.
[Edit] And don't we all fill the bath only part way up? Otherwise all the water above a certain level would flow over the sides when you stepped in the bath. Makes sense that she wouldn't fill the bath completely, or she'd lose some of the water when she stepped into it.
yes, but they ask specifically how long it would take to fill the tub completely...
latest conundrum
I'm sorry, but i think all u guys missed the fact that it said "1.5mm of depth per minute"... as in 1.5mm times the area of the tub per min... therefore (4.19(volume of sphere) divided by 0.015 x 7.38 (ice melted per min)) it would only take 37.8 (round to 38) minutes to melt all the ice and 53.3 (round to 54) minutes to fill the tub if there was enough ice.
altoid wrote:Anybody know what time they update with the new puzzle?
They try to do it at a different time each time to make it fair for people in different time zones, so everyone has a chance at being first.
It's a long shot... but ... instead of calculating how much it would be... have the answer s "Never" maybe the round up parts and stuff are red herrings...
I'm not gonna submit my answer till tomorrow tho.
and when i say never . i mean Never assuming what they provide is what you have to work with.
(am i making sense?)
one thing that i have noticed is that everyone seems to be forgeting the fact that each minute less volume of ice is melting. It starts at 4,188,790,204.78639mm^3 in the first minute 18,821,295.72482mm^3 melts from the 1.5mm that melts. Well that changes the radius from 1000mm to 998.5mm making the volume of this sphere 4,169,968,909.06157mm^3. So in the 2nd minute less volume will melt, which is 18,821,295.72482mm^3. That is 56,463.84476mm^3 less then what melted in the first minute.
It will take 667 (1/0.0015) minutes for the sphere to melt, but it won't completely fill the tub unless the volume of the princess is about 0.4877 cubic meters, and she's already in the tub. Of course, if she's larger than that, it will take less time. Anybody know how big the princess is?
If you know the volume (4.6765 > V > 0.4877 cubic meters) of the princess, then the time is:
[1 - (1 + [V - 2.7*sqrt(3)] * 3/[4*PI])^(1/3)] / 0.0015 minutes
What?
So, what in fact is the answer? I want some of those NP.
Re: latest conundrum
FyerBug wrote:I'm sorry, but i think all u guys missed the fact that it said "1.5mm of depth per minute"... as in 1.5mm times the area of the tub per min... therefore (4.19(volume of sphere) divided by 0.015 x 7.38 (ice melted per min)) it would only take 37.8 (round to 38) minutes to melt all the ice and 53.3 (round to 54) minutes to fill the tub if there was enough ice.
1.5 mm of depth, as in the top 1.5 mm layer of ice, not 1.5 mm of water in the tub. Because of this, also, less volume of ice is melting, but volume doesn't matter for the actual melting. The top 1.5 mm of ice melts every minute, it doesn't matter how much volume that is.
All that matters for the length of time is how long it takes the radius of the ice sphere to melt, and that's 667 minutes. (1 m / 0.0015 m == 666.6666(etc) ) Since the ice sphere has less volume than the tub, all that matters is how long it takes the ice to melt, so the answer is 667.
Hi! I'm new to the forum and i hope i can help you as you can help me =)
well,
this is what I got
The volume for a hexagonal solid is V=2,5981hL^2, where h is the height and L is the side measure. So my bath's volume is:
V(bath) = 2,9930112 m^3
and the sphere volume is: Vs = 4,18879 m^3
Since the ice melts in a uniform rate of 1,5 mm per minute, we use this formula to the correspondet volume:
V = (4/3)pi (R-x)^3 , where x is the amount of ice that already melted.
2,9930112=(4/3)pi(1-x)^3
x=0,1059950758 m
so the bath will be completely full when the ice sphere has lost 0,1059950758 meters os radius.
The next thing is to calculate the minutes
t= 0,1059950758/(1,5*10^-3) = 70,66338388 minutes
they say to round up, so my answer is 71 minutes.
what do you say? am I wrong? because it seams that our answers are very different.
sgaileach wrote:Hi! I'm new to the forum and i hope i can help you as you can help me =)
well,
this is what I got
The volume for a hexagonal solid is V=2,5981hL^2, where h is the height and L is the side measure. So my bath's volume is:
V(bath) = 2,9930112 m^3
and the sphere volume is: Vs = 4,18879 m^3
Since the ice melts in a uniform rate of 1,5 mm per minute, we use this formula to the correspondet volume:
V = (4/3)pi (R-x)^3 , where x is the amount of ice that already melted.
2,9930112=(4/3)pi(1-x)^3
x=0,1059950758 m
so the bath will be completely full when the ice sphere has lost 0,1059950758 meters os radius.
The next thing is to calculate the minutes
t= 0,1059950758/(1,5*10^-3) = 70,66338388 minutes
they say to round up, so my answer is 71 minutes.
what do you say? am I wrong? because it seams that our answers are very different.
Try doing the calculation for the volume of the bath in steps:
2.5981*0.8 = 2.07848
2.07848 * (1.5^2) = 2.07848 * 2.25 = 4.67658
Since this throws off most of your equations, I hate to say it, but you are mistaken. And since the volume of the tub is greater than the volume of the sphere, all that matters is how long it takes for the sphere to melt. Since the ice melts uniformly at 1.5mm per minute, and the radius is 1 m, the answer is 1 m / 0.0015 m = 667 minutes.
Nique, you're assuming that the tub is "completely full" when the ice sphere melts. I think a more likely assumption is what most others have made, that it's "completely full" when it's filled to the brim with water.
