You are trying to figure out how many gumballs you need to fill a 7.3 x 5.0 x 9.4 rectangular box for Halloween. Each gumball ha
s a radius of 1/2 in, if the packing density for spheres is 5/8 of the volume will be filled with gumballs while the rest will be air how many gumballs will be needed? Round to the nearest whole number.
According to the calculations made, 410 gumballs will be needed to fill the box.
Since you are trying to figure out how many gumballs you need to fill a 7.3 x 5.0 x 9.4 rectangular box for Halloween, and each gumball has a radius of 1/2 in, if the packing density for spheres is 5/8 of the volume will be filled with gumballs while the rest will be air how many gumballs will be needed, to determine this amount the following calculation must be performed:
(Volume of box x 5/8) / volume of gumballs = Amount of gumballs
Volume of a sphere = 4/3 x 3.14 x (radius x radius x radius)
Volume of a gumball = 4/3 x 3.14 x (0.5 x 0.5 x 0.5) = 0.5235 inches
((7.3 x 5 x 9.4) x 5/8) / 0.523 = X
(343.1 x 5/8) / 0.523 = X
214.4375 / 0.523 = X
410 = X
Therefore, 410 gumballs will be needed to fill the box.
