Given parameters:
Diameter of the malt balls = 0.8in
Dimensions of the prism = 4in x 3in x 7.5in
Unknown:
Number of malt balls that will fit in the carton = ?
Solution:
To solve this problem, we need to find the volume of each of the malt balls, and then the volume of the rectangular prism.
Volume of the malt balls = [tex]\frac{4}{3} \pi r^{3}[/tex]
This is because we assume that the balls have a spherical shape.
Where r is radius and π is a constant
Radius of the malt balls = [tex]\frac{0.8}{2}[/tex] = 0.4in
So, volume = [tex]\frac{4}{3} x 3.142 x 0.4^{3}[/tex] = 0.27in³
Volume of the rectangular prism = l x w x h
where l is the length
w is the width
h is the height
So the volume is 4 x 3 x 7.5 = 90in³
The number of malt balls that can be packed here = [tex]\frac{90}{0.27}[/tex] = 333 malt balls
