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?

Answer 1

1.33 cm

Step-by-step explanation:

Mass of copper,
`m=243 g`

Side of the cube,
`a=3 cm`

Volume of the copper cube,
`a^3=(3cm)^3=27cm^3`

Density of copper,
`density =(mass)/(volume)`

`\rho=(243gm)/(27cm^3)=9gm/cm^3`

Let the radius of the sphere be r.

Volume of the copper sphere,
`V=(4)/(3)\pi r^3`

`V=(m)/(\rho)\\\Rightarrow (4)/(3)\pi r^3= (m)/(\rho)\\\Rightarrow r =\sqrt[3]{ {(3m)/(4\pi \rho)}}`

If the mass is 50 g, then the radius of the copper sphere is:

`r=\sqrt[3]{(3* 50g)/(4\pi 9g/cm^3)} =1.33 cm`