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  = $\frac{4}{3} \pi r^{3}$

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  = $\frac{0.8}{2}$   = 0.4in

So, volume  = $\frac{4}{3} x 3.142 x 0.4^{3}$   = 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 = $\frac{90}{0.27}$   = 333 malt balls