Ice Cream Scoop

Ok, here's the scenario : Say you bought a scoop of ice cream in a cone. The scoop wasn't large or small, it was just a regular scoop. You then accidentally leave it out in the sun too long and it melts. Will the scoop of ice cream that is now melted overflow the cone or will it stay inside the cone and not overflow?

Wayyy too many variables here.

Exactly what kind of cone is it? Is it a standard cone or a waffle cone?
Since you "accidentally" left it in the sun, is it assumed that the cone is completely verticle or on its side? If it's a waffle cone, is it propped vertical?

Wayyy too many variables here.

Exactly what kind of cone is it? Is it a standard cone or a waffle cone?
Since you "accidentally" left it in the sun, is it assumed that the cone is completely verticle or on its side? If it's a waffle cone, is it propped vertical?

Standard cone. Vertical because you were holding it and didn't eat it fast enough, so it melted. Be warned, there's math in this =P

Still not enough information. Perfectly spherical scoop? Diameter of scoop equal to the diameter of the cone? Angle of the cone? Does the density of the scoop change as it melts?


I'm assuming it looks like this, and the density is constant?
Volume of scoop = 4/3 pi r^3
Volume of cone = 1/3 pi r^3 * cos theta / tan theta

If the angle of the cone is less than 17.6 degrees, the cone can contain the scoop

The scoop is not a cube but a regular scoop of ice cream. Regular scoops of ice cream are spherical. Since the scoop is also regular, you must imagine what a regular scoop diameter is and a regular cone diameter. There is an actual measurement though. The cone is not oblique. The angle is 90 degrees.

Btw, you're on the right track with the volumes.

It's going to overflow. Because the outside and top of the icecream will melt before the inside/bottom. The melted ice cream will then drip down to the side, over the cone, and then to your hand. Which will now be sticky. (and icky!)

Might as well have us guess the exact mass of the scoop of ice cream.

all scoops of ice cream i ever saw had varying sizes of holes in the middle depending on scooper skill. believe this would be average for a scoop of ice cream? this would mean measured volume based on radius etc did not correspond to actual mass. what size is the hole in the middle of this average scoop?

What the pineapple is a regular cone diameter? Then pomegranate, I want my motherpineappleing cone to be as big as possible. Give us variables, peach!

nigguh we be haulin em 1 foot wide waffle cones here in canada

nigguh we be haulin em 1 foot wide waffle cones here in canada

This is the Rubik's Cube, not the funhouse .

It's going to overflow. Because the outside and top of the icecream will melt before the inside/bottom. The melted ice cream will then drip down to the side, over the cone, and then to your hand. Which will now be sticky. (and icky!)

Ice Cream Solved.
I second the thought that the ice cream will melt outside to inside-
THus leaving a soggy cone left.
Also are we taking the idea of the soggy cone decay into consideration?

The scoop is not a cube but a regular scoop of ice cream. Regular scoops of ice cream are spherical. Since the scoop is also regular, you must imagine what a regular scoop diameter is and a regular cone diameter. There is an actual measurement though. The cone is not oblique. The angle is 90 degrees.

Btw, you're on the right track with the volumes.

[color="#cc8899"]
Regular scoops of ice cream are not spherical - maybe the top half, but at some point the upward motion of the scoop results in a nonspherical edge, usually a flat surface, or some kind of jagged slope. This is usually the end placed downwards in the cone.[/COLOR]

Even getting one scoop of ice cream, it's usually packed into the cone, not just placed on it. And how big is this cone? Is it twice the size of the scoop? Smaller? What's the radius of the base? If you want the answer to have numbers, you have to give numbers yourself.

The scoop is not a perfect circle and would probably sink into the the cone. If the ice cream were to miraculously levitate in the cone, then it would overflow. But ice cream doesn't work like that. Unless you ate part of the cone, the ice cream would melt within the cone and collect in the bottom.

The scoop is not a perfect circle and would probably sink into the the cone. If the ice cream were to miraculously levitate in the cone, then it would overflow. But ice cream doesn't work like that. Unless you ate part of the cone, the ice cream would melt within the cone and collect in the bottom.

Only if the ice cream didn't extend outwards from the mouth of the cone to begin with. If the scoop was already larger than the rim of the cone, than its drippings would fall on a now-sticky hand.

Using Dusk's picture as reference, the scoop would not overflow, but there will be streaks of melted ice cream flow down just because the scoop is not inside the cone entirely, or in other words overflow. Since you said it's not a small scoop, the latter is impossible.