To find the volume of the cube, we need to raise the side length to the power of 3: 7 mm * 7 mm * 7 mm = <<7*7*7=343>>343 mm^3
The hole in the middle doesn't change the volume of the cube, so we can ignore it.
To convert from mm^3 to cubic meters, we need to multiply by the conversion factor 1 meter / 1,000,000 mm cubed: 343 mm^3 * 1 m / 1,000,000 mm^3 = 0.000343 m^3
To find the cost of one prototype, we need to multiply the volume of the cube by the cost per cubic meter: 0.000343 m^3 * $270 / m^3 = $92.61.
To find the total cost of the prototypes, we multiply the cost per prototype by the number of prototypes: $92.61 per prototype * 1,000,000 prototypes = $<<92610000=92610000>>92,610,000. Answer: \boxed{92,610,000}.
A toy manufacturer has designed a new piece for use in building models . It is a cube with side length 7 mm and it has a 3 mm diameter circular hole cut through the middle. The manufacture wants 1,000,000 prototypes. If the plastic used to create the piece costs $270 per cubic meter, how much will the prototypes cost? Be exact.
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