Question

A chocolate company makes chocolate malt balls that are 0.8 inches in diameter. The carton they are to be packed in is approximately a rectangular prism with the dimensions 4 inches by 3 inches by 7.5 inches. How many malt balls will fit in the

Answer 1

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 =
`(4)/(3) \pi r^(3)`

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 =
`(0.8)/(2)` = 0.4in

So, volume =
`(4)/(3) x 3.142 x 0.4^(3)` = 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 =
`(90)/(0.27)` = 333 malt balls