What would be the best boat to construct to hold the most pennies, with a sheet of 15cm x 15cm aluminum foil?

Question

It needs to be shaped either like a square or rectangle, NO circles or any other shapes that the measurement cant be read accurately for volume.

it does not have the be the same height all around...


im looking for it to hold atleast 50 pennies.

i only have a 15 CENTIMETER by 15 CENTIMETER sheet to work with.


i like you idea but i already tried that. i just wanted to know if there was a trick or something.

Answer 1

Place the foil on an upside down cookie sheet or some other flat surface which will support your loaded container as you place it into the water
Place 49 pennies in a 7 x 7 square perfectly centered on your foil.
Fold up the sides.
This will give you a container measuring 13.3 cm x 13.3 cm x .85 cm high.
The volume of this container will be 150.3 cubic cm.
1 cubic cm of water weighs 1gram.
Therefore this container could hold 150.3 grams less the weight of the foil itself and still remain boyant.
The weight of a penny is 2.75 grams.
The container will theoretically hold a maximum of 54 pennies. The only question is whether the sides would be sturdy enough to hold back the pressure of the water without collapsing. Sorry don't have the necessary information on the foil to perform this calculation. Here's where trial and error kicks in, good luck.

Answer 2

Your boat needs to displace the maximum amount of water using the least amount of material. Although someone mentioned that is a sphere, obviously you can't use a sphere. The next best shape would be a perfect cube with the top open (to maximize material use). I won't do the calculus for you, but believe me when I say you reach maximum water displacement given a perfect cube compared to any other shaped cube. This is how I would approximate a perfect cube using all of the material:

I would cut 4x4 squares out of each of the 4 corners of your 15x15 sheet. You'll be left with what looks like a fat cross. Fold the sides up to make an open top box with 7cm long sides. Cut each of the 4 squares in half (eight 4X2 rectangles), and fasten them end to end to make four 8X2 rectangles. These 8X2 rectangles squares can now be fastened to the top of the open box to make it a more perfect cube. The bottom with be 7x7cm, and it will stand 6cm tall. Not a perfect cube, but about as close as you'll get.

Since it's just make of aluminum foil, use just good old tape to fasten the pieces together.

You might want to stack the pennies as close to the sides as possible. Otherwise, the sides might collapse if you put the pennies all in the middle (like a mound). That would be bad.

Good luck!

Answer 3

FOLD EACH SIDE IN 2.5 CM
THIS IS WHY

V= L * W* h
substitute
V= (15-2x)(15-2x)(x)
distribute
V= (225-30x-30x+4(x)^2) (x)
re-arrange
V= (4(x)^2 -60x +225) (x)
simplify
V= 4(x)^3 - 60(x)^2 + 225x
take the first derivative
V'= 12(x)^2 - 120x + 225

set derivative = 0
12(x)^2 - 120x + 225=0
solve for x
using the quadratic formula or factoring

......x=7.5 & x=2.5...... (these are critical points) when substituted into derivative = 0
Find minimum or maximum point through Derivative Test.
Derivative test, this is homework!!

x=7.5 is minimum resistance
x=2.5 is MAXIMUM resistance

Therefore FOLD THE 15X15cm square IN 2.5CM
EACH SIDE...

need extra notes for this?
email me [e-mail]

I was thought this in a AP Readiness program at UCLA
For high school students

Answer 4

If you get to arrange the pennies in the boat,
go for a square shape 5 x 5 pennies in size.
Two full layers on the bottom will be 50 pennies.
That way you maximize the wall height for best
buoyancy.

Answer 5

The best boat would be one that has a low center of gravity on the water, yet has high enough walls on either side to support 50 pennies.

You will probably find that a boat with one to one and a half inch walls should be fine. Ensure to double back on the walls ensuring they are thickness as well as pinch the corners over to seal them off. Your boat should be square.

Answer 6

You do not specify if it has to float.

The most efficient shape is a sphere - even if you have to cut a few bits off to make it.

Or consider half a sphere. It just might float...

A sphere holds more volme than any other 3 dimensional shape, so use that as your opening hypothesis.

You can measure volume easily by filling your empty shape with water and measuring that.

Answer 7

build your boat so u have a maximum amount of foil in contact with the water. a rectangular boat with very low sides is ideal