Question
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.
Answers
GPT 3.5
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}.
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}.