Achocolate company makes chocolate malt balls that are 0.75 inches in diameter. the carton they are to be packed in is approximately a rectangular prism with the dimensions 3 inches by 3 inches by 7.5 inches. how many malt balls will fit in the carton?
(reminder: you can assume that for random packing space 190% of the volume of the sphere is needed to pack the spheres and volume if sphere is 4/3π x r^3)
a. 160 balls
b. 210 balls
c. 305 balls
d. 82 balls

A. 160 balls

Step-by-step explanation:

First we find the volume of each sphere.

diameter = d = 0.75 in.

radius = r = d/2 = 0.75/2 in. = 0.375 in.

V = (4/3)π(r^3) = (4/3)(3.14159)(0.375 in.)^3 = 0.221 in.^3

Because of the assumption about the space occupied by a sphere in random packing, we now calculate 190% of the volume of the sphere.

190%V = 1.9 * 0.221 in.^3 = 0.420 in.^3

Now we calculate the volume of the box.

V = LWH = 3 in. * 3 in. * 7.5 in. = 67.5 in.^3

To find out the number of balls that fit in the box, we divide the volume of the box by the randomly packed ball volume.

number of balls = (67.5 in.^3)/(0.420 in.^3) = 160.8

160 balls

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional