Question

The company wants to use the package that has the least amount of wasted space. The company should choose the prism because it has approximately 11. 6 in. 3 less wasted space than the cylinder. The prism because it has approximately 14. 1 in. 3 less wasted space than the cylinder. The cylinder because it has approximately 11. 6 in. 3 less wasted space than the prism. The cylinder because it has approximately 14. 1 in. 3 less wasted space than the prism

Answer 1

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.

What is volume?

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,

$=2 \times \dfrac43 \times \pi r^3 \\\\= 28.2743\rm\ in^3$

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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