Question

A chocolate company makes chocolate malt balls that have a radius of 0.34

inches. The carton they are to be packed in is approximately a rectangular prism with
dimensions 1.5 inches by 2.5 inches by 6 inches. How many malt balls will fit in the
carton

Answer 1

Approximately 141 malt balls

Explanation:

this problem is on the mensuration of solids shapes.

first we need to calculate the volume of the rectangular prism

volume of prsim= l*b*h

given that

length= 1.5 in

breath=2.5 in

hieght= 6 in

volume= 1.5*2.5*6

volume=22.5 in^3

secondly we then calculate the volume of a malt ball

given that

raduis r= 0.34

volume of sphere = 4/3πr^3

volume of sphere = 4/3*3.124*(0.34)^3

volume of sphere = 1.33*3.142*0.039

volume of sphere = 0.16 in^3

now we can calculate the amount of sphere that can fit into the prism as

= volume of prism/volume of sphere

= 22.5/0.16

=140.6

approximately 141 malt balls