HeLP! please help me solve this math problem...?

Question

ok. my math teacher says that whoever can solve this problem get like 100 xtrra credit points..and i need it like reall bad..i asked my dad ..i tried it myself and i couldnt even get a REASONABLE anwser...so HELP! please... =/

QUESTION: approx. how many corks are in this barrel?

about the barrel..

width (at top and bottom):14 7/8"
bilge(width at widest point): 18 1/2"
capacity: 16 gallons
stave thickness: 3/4"
bottom thickness:1"


ABOUT THE CORKS:
they vary from 1 1/2" to 2" in size
estimated average cork lenght: 1 11/16
diameter of corks: 13/16
(corks may swell after being pulled out:)

good luck on this one...it like so hard.

please help on this one..and dont give me random numbers.
the answer may not be exact but its should be about the estimate!!! thnxs.... =)

whoever has the closest number gets to be BEST answer.. thnxs. again..!

~~~~~~~~~~~~~~~=)

Answer 1

since 1 gallon = 231 cubic inches:

volume of barrel = 16 gallons = 3696 cubic inches

volume of cork = length* PI * radius^2
= 1 11/16 * PI * 13/32^2
~ 0.8749 cubic inches

barrel vol / cork vol = 4224.269
= max corks in barrel if no space left.
if we divide by 1.1 (as suggested above), we get about
3840 corks.

I just figured out why my answer is different than the one above. The cork area (cross section) should be pi*r^2, not 2pi*r^2.
Isn't it? Right? Area of a circle? Am I right?

Answer 2

I see no one has tryed to help you. The way I would do this problem is to use liquid, you know you have a barrel that holds 16 gallons. Find how many ounces are in 16 gallons of water. how many ounces of water will a contaner of 1 3/16" by 2" hold, devide this into 16 gallons and that should be very close to how many corks or in the barrel. Good luck and hope you get your extra 100 points. Oh one you can give your math teacher is, how many dimes will fit in a quart milk bottle. answer is 620. Happy New Year. When I started on this problem there were no answers, now there is 4 others. and one has the same Idea as I about solving it.

Answer 3

The barrel holds 16 gallons. All of the other measurements are academic (probably to make the problem seem more difficult than it actually is!) A gallon (liquid measure) is 231.0 cu. in. in volume - therefore the barrel is
231*16 or 3696 cu. in.
The corks are 1 11/16" X 13/16". And each cork will be PiR^2*H or 3.142*0.406^2 which is 0.518 cu. in. for each cork.
There will be space in the barrel which will necessarily be between the corks. Since the corks are more or less round, this space will be approximately 21% of the barrel.
(This is determined by drawing a 1" square and inscribing a 1" diameter circle inside of it. The 1" is 1 sq. in. and the circle is 0.785 sq.in. - the difference is "wasted" space not taken up by the diameter of the corks.)
If we assume another 5% of wasted space due to the corks not being exactly stacked on top of each other - we have a total of space in the barrel that is not taken up by the corks of approximately 26%. If we assume another 3% for the corks "swelling" after being pulled out, we have 71% of the barrel volume for the corks.
0.71*3696 0r 2624 cu.in. in the barrel for the corks.
2624/0.518 = 5066 corks.

Don't spend all of your extra credit in one place.

Answer 4

The only hard part of this problem is figuring the volume of the barrel. Add the width of the top to the width at the bilge and divide by two. Then divide by 2 again to get the radius. Then multiply the average radius that you've just calculated, square that, them multiply that times 3.14, then multiply that times the height. This will give you the volume of the barrel. Calculate the volume of the average cork and divide that into the volume of the barrel and you will get an answer that is close but a little too large. Divide the answer by 1.1 and you will certainly be in the ball park of extra credit.

Answer 5

cork length = 1 11/16 in = 4.28625 cm
cork diameter = 13/16 in = 2.06375 cm
cork radius = 2.06375 / 2 = 1.031875 cm
cork area = 2 (Pi) r^2 = 2 (Pi) 1.031875^2 = 6.69 cm^2
cork volume = 6.69 * 4.28625 = 28.675 cm^3

barrel volume = 16 gallons = 16 * 3.78 L = 60.48 L = 60480 cm^3

number of corks that would fit the barrel is approx. 2109.