1. ## [SOLVED] Jar

edit: wasn't supposed to post that question

2. Originally Posted by gxxtreme
I have a word problem that I'm trying to figure out. There is a jar filled with jelly beans, and I'm supposed to figure out how many are in there. The jar is like a frustum shape, with the bottom radius being the smaller one. I cannot see or touch the jar. I only have two pictures of it; one from the side, and one from the top. I need to know what is the most efficient and most accurate way of getting the answer.
Since you use the word "frustrum" I assume you know that this is the frustrum of a cone. This website: Volume of a Frustum of a Cone
gives the volume as $V= \frac{\pi h}{3}(r^2+ rR+ R^2)$ where "r" and "R" are the radii of the two bases and h is the vertical height of the cone.

Once you have that, you will need to estimate the volume of a single jellybean and divide one volume by the other.

3. Originally Posted by gxxtreme
I have a word problem that I'm trying to figure out. There is a jar filled with jelly beans, and I'm supposed to figure out how many are in there. The jar is like a frustum shape, with the bottom radius being the smaller one. I cannot see or touch the jar. I only have two pictures of it; one from the side, and one from the top. I need to know what is the most efficient and most accurate way of getting the answer.
as HallsofIvy stated:
Once you have that, you will need to estimate the volume of a single jellybean
and you'll need to account for the volume lost in the space BETWEEN the jelly beans
and divide one volume by the other.
If the picture shows some jelly beans, then scale the size of a jelly bean. You may need to scale the length & width of a dozen or more to have a reasonable "average" size jelly bean.
Use that scaled jelly bean to determine the diameter of the top and bottom radius and height of the frustrum & then make your calculations.

You may want to buy a bag of jelly beans, measure a cup full and then count them.

THEN (this is the fun part) mash/smash/pulverise/compress as many jelly beans as possible into the cup.
(YOU NEED TO COUNT THEM BEFORE YOU SQUEEZE'M)

With that you can account for the lost space between the beans, and thus estimate somewhat more acccurately than just a WAG.

.

4. Originally Posted by aidan
as HallsofIvy stated:
and you'll need to account for the volume lost in the space BETWEEN the jelly beans

If the picture shows some jelly beans, then scale the size of a jelly bean. You may need to scale the length & width of a dozen or more to have a reasonable "average" size jelly bean.
Use that scaled jelly bean to determine the diameter of the top and bottom radius and height of the frustrum & then make your calculations.

You may want to buy a bag of jelly beans, measure a cup full and then count them.

THEN (this is the fun part) mash/smash/pulverise/compress as many jelly beans as possible into the cup.
(YOU NEED TO COUNT THEM BEFORE YOU SQUEEZE'M)

With that you can account for the lost space between the beans, and thus estimate somewhat more acccurately than just a WAG.

.
Why do the mashing? (I certainly wouldn't want to have to eat that mass of jelly beans!) Just count the number of jelly beans in our cup, then fill the cup with water to determine the number of square inches, perhaps by pouring from the measuring cup into a square pan. That should give you the volume of that many jelly beans including air space.

5. Nice ideas. Thanks guys.