Volume is a three-dimensional scalar quantity. The company should choose the cylinder because it has approximately 11.6in³ less wasted space than the prism.
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the two balls with a radius of 1.5 inches is,
[tex]=2 \times \dfrac43 \times \pi r^3 \\\\= 28.2743\rm\ in^3[/tex]
The Volume of the prism with dimensions 6in × 3in × 3in are,
Volume of the prism = 6in × 3in × 3in = 54 in³
The volume of the cylindrical box with a radius of 1.5 in and a height of 6 inches is,
Volume of Cylinder = πr²h = π × (1.5)² × 6 = 42.4115 in³
Wasted volume in Prism, when two balls are inside,
Wasted Volume = 54in³ - 28.27in³ = 25.72566 in³
Wasted Volume in Cylinder, when two balls are inside,
Wasted Volume = 42.4115in³ - 28.27in³ = 14.137 in³
The difference in the waste volume of prism and cylinder,
Difference = 25.72566in³ - 14.137in³ = 11.6in³
Hence, The company should choose the cylinder because it has approximately 11.6in³ less wasted space than the prism.
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