Please help...The cone has a diameter at its base of 30cm and it is 45 cm tall. if a piece of ancy is 2 cm long, 1cm wide. how many pieces of candy can be put in the cone? I did figure that the volume of the cone was 10494.53....need help
Please help...The cone has a diameter at its base of 30cm and it is 45 cm tall. if a piece of ancy is 2 cm long, 1cm wide. how many pieces of candy can be put in the cone? I did figure that the volume of the cone was 10494.53....need help
IF you can get 100% density,
you could divide the volume of a single piece of candy into the total volume of the cone.
(Re-compute your volume).
It appears that the candy would be 1cm diameter by 2cm length, which would give 1.57cc per piece of candy.
That would give the MAXIMUM possible number of pieces of candy in the cone.
Most likely, the candy will be dumped & loosely placed into the cone. Will the cone have a small opening at the apex in which to fill the cone or will the base of the cone be open? Is the candy piece unwrapped? If wrapped in someting, is it tightly wrapped or does it have an exposed paper twist at the ends?
You will lose volume of the available space due to the loose packing of the candy pieces & wrapper, if any. You will need to determine the packing density of the candy for a given volume. There is a lot of data for such on the internet.
Do you own estimate:
Determine the volume available (re-check your number as it does not agree with volume of a standard cone with those values given).
If I were doing this:
1) get a measuring cup
2) count the number of pieces that fill 1 cup.
3) count the number of pieces that fill to 2 cup measure.
then
4) measure a small box (a 10x10x10 in centimeters) and count the number of pieces required to fill it.
5) measure a box that is two to three(or 4 times ) that volume and count the pieces.
What that will do:
it will give you an approximation of the "LOSS" due to the space between the pieces of candy.
You can guess that the volume available is cubic, that is the number of cubic cc's possible.
Then, guess that your candy is a ball that will fit inside 1 cubic centimeter. Determine how many spheres will be required to equal 1 (one) piece of candy. Use that ratio to guess the total pieces of candy you could place in the cone.
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Aidan has clarified . Well , assuming those candies are perfect cylinders , with radius , 0.5 cm and length 2 cm .
Then the volume of the candy would be
$\displaystyle V=\pi (0.5)^2(2)=0.5\pi$
Then the volume of cone ,
$\displaystyle V=\frac{1}{3}\pi (15)^2(45)$
$\displaystyle =3375\pi$
so number of candies that can be fit into that cone would be
$\displaystyle \frac{3375\pi}{0.5\pi}=6750$ pieces .