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?
Since the volume of a cube is s^3, s being the side. Therefore
3^3=27 cubic cm. the volume od the cube. But the mass of this cube is 243 grams, therefore:
Density=mass/volume
Density=243/27=9 grams/cm^3
Volume of a sphere is=4/3.Pi.r^3, r=radius, But we have:
Mass=Volume X Density
Mass=4/3.Pi.r^3.9, therefore,
r^3=Mass/(4/3.Pi.9) =243/(4/3.3.141592.9)=37.7cm, so
r^3=37.7cm^3
r=3.35cm-radius of a 243g sphere of copper.
50g=4/3.Pi.r^3.9
r=1.10cm-radius of 50g sphere of copper.
Changing the material would change the function, because its density would be different.
