A factory needs to produce ball bearings with a diameter of 6 cm. How many cubic centimeters of metal are needed to make 3000 ball bearings?

339,292 cm³

Step-by-step explanation:

Assume that each ball bearing is a perfect sphere and that no material is wasted during the production.

The volume of a sphere is:

If each ball bearing has a diameter of 6 cm (radius of 3 cm), the individual volume is:

For 3,000 ball bearings:

339,292 cm³ of metal are needed to make 3,000 ball bearings.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form