Question

A manufacturer wants to make a ball bearing that is made of a mixture of zinc, iron, and copper and has come down to a choice of two alloys. Alloy A has a density of 7.5 grams per cubic centimeter and alloy B has a density of 8.5 grams per cubic centimeter.

Use the formula for the volume of a sphere, V=43πr3 , and the formula for density, D=mv , to write an equation for m as a function of r for each alloy.

Answer 1

• Alloy A: m = 10πr³ . . . . . . . . . . . . mass in grams; radius in cm
• Alloy B: m = (34π/3)r³

Explanation:

Solving the density equation for mass, we get ...

D = m/V

m = DV . . . . . multiply by volume

Substituting the volume formula gives ...

m = D(4/3π)r³

Alloy A

Substituting D = 7.5 gives ...

m = 7.5(4/3)πr³

m = 10πr³ . . . . . simplify

__

Alloy B

Substituting D = 8.5 gives ...

m = 8.5(4/3π)r³

m = (34π/3)r³ . . . . . simplify