<span>(box volume/ball volume) * packing density = # mables that fit in box
max packing density is pi/3*sqrt(2) for spheres, according to the Kepler conjecture, so if ball volume is b,
(4.5 * 4.5 * 7.5 / b) * (pi/3*sqrt(2)) = 160
151.875 / b * (pi/3*sqrt(2)) = 160
151.875 * pi / b * 3 * sqrt(2) = 160
50.625 * pi / b * sqrt(2) = 160
10.125 * pi / 32 * sqrt(2) = b
b ~ 0.7
For a tin cylinder of 4.5 diameter, the volume is (4.5/2)^2 * pi * h. Using the formula again,
(box volume/ball volume) * packing density = # mables
(5.0625 * pi * h / (10.125 * pi / 32 * sqrt(2)) * (pi/3*sqrt(2)) = 160
(5.0625 * pi * h * 32 * sqrt(2) / 10.125 * pi) * (pi/3*sqrt(2)) = 160
5.0625 * h * 32 * sqrt(2) / 10.125 * (pi/3*sqrt(2)) = 160
162 * h * sqrt(2) * pi / 10.125 * 3 * sqrt(2) = 160
54 * h * pi / 10.125 = 160
54 * h * pi = 1620
h * pi = 30
h = 30/pi
h ~ 9.55
So if the marbles are of equal size, and both the box and cylinder are packed as tightly as possible, the cylinder would have to be 9.55 units tall.</span>
62.5%, Because you do 5 divided by 8 that would be 0.625. move te decimal over two places and you have your percent.
You, too, can read the graph and determine that the second selection is appropriate. Or, you can graph it yourself and determine the (one) correct solution.
Answer:
ummmmmmmmmm I known I'm NOT gonna get 100 points but it's 4
Answer:
It is the third option. I just got it correct.
Step-by-step explanation:
