geometry q

Hooray crowd-sourcing

The jar is approximately 8x8x8, basically a cube.

It’s filled with regulation-sized Hersey’s Kisses.

How many would you estimate are in there? :slight_smile:

One website I found says a Kiss is approx 1 inch tall and 3/4 inch in diameter at the base.

8x8x8 what?

that would help, wouldn’t it. 8 inches all around (err all cube)

Assume a cone.

V=pi/3rrh
V= .375
.3751 = 0.14 cu in.
Vc = 8
8*8 = 512

512/.14= 3657

So now estimate what the ratio of dead space to chocolate is and multiply that by 3657 for your answer.

That can’t be right, can it? If the area of the cube is 512 cubic inches and you’re putting in 1 inch tall cones, you’re not getting thousands in?

Assuming your dimensions for the Kiss are correct and the chocolate is perfectly packed into the container and filling it 100%, then, yes, about 3657 Kisses is the right answer.

The thing is, you know they aren’t perfectly packed in - the Kisses will incompletely pack into the corners, some will be sideways, or tilted on an angle, etc. They are, in fact, only occupying some fraction of container.

If you can get a visual estimate of the container and get a sense of how much of it is air and how much is chocolate, then you can determine how many Kisses are actually there. Let’s say it’s 50-50; in that case, you have about 1828 Kisses.
8 inches is pretty big - think about it; if you line up Kisses with 3/4" (.750") diameters to make a line 8 inches long, you need to use 10 Kisses (8/0.750 = 10.66…). Expand that to three dimensions, and the number doesn’t seem so crazy anymore.

ETA: The volume of the cube is 512 cubic inches. The area is 8x8=64 cubic inches.