Question

A toy manufacture has designed a new part for use in building models. The part is a cube with side length 14 mm and it has a 12 mm diameter circular hole cut through the middle. The manufacture wants 9,000 prototypes. If the plastic used to create the part costs $0.07 per cubic millimeter, how much will the plastic for the prototypes cost? Round to two decimal place

Answer 1

The volume of the cube with a side length of 14 mm is 14 x 14 x 14 = 2744 cubic mm. The volume of the cylindrical hole with a diameter of 12 mm and a height of 14 mm (equal to the side length of the cube) is (π/4) x 12 x 12 x 14 = 6048π/4 cubic mm = 1512π cubic mm.

The total volume of the cube with the hole is the volume of the cube minus the volume of the hole: 2744 - 1512π cubic mm.

The total plastic used for 1 prototype is the total volume of the cube with the hole multiplied by the cost per cubic mm: (2744 - 1512π) x 0.07 = 117.64 - 65.71π dollars.

To find the total cost of plastic for 9,000 prototypes, we multiply the cost of one prototype by 9,000: (117.64 - 65.71π) x 9,000 = 1,058,760.35 - 591,439.8π dollars.

Rounding to two decimal places, the plastic for the prototypes will cost approximately $472,344.78.