I got this problem wrong on my homework so I want to know what I did wrong. Can someone help me?

Question

The side length of a 243-gram copper cube is 3 centimeters. Use this information to write a model for the radius of a copper sphere as a function of its mass. Then, find the radius of a copper sphere with a mass of 50 grams. How would changing the material affect the function?

(volume: v=4/3πr^3)

Answer 1

The density is the mass divided by the volume.  The mass of the copper cube is given as 243 grams.  The volume of the 3 cm cube is 3³ = 27 cm³.

 

Density = 243 g/27 cm³ = 8.96 g/cm³

 

The volume of a sphere is 4*pi*r³/3.  Volume* density = mass, so:

 

(4*pi*r³/3)*(8.96 g/cm3) = m

 

Solving for r:

 

r = (3m/4*pi*8.96)^1/3 ≅ (0.0267m)^1/3

 

For m = 50 grams:

 

r = (0.0267*50)^1/3 = (1.335)^1/3 = 1.101 cm