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

Answer:

1.33 cm          

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, $density =\frac{mass}{volume}$

$\rho=\frac{243gm}{27cm^3}=9gm/cm^3$

Let the radius of the sphere be r.

Volume of the copper sphere, $V=\frac{4}{3}\pi r^3$

$V=\frac{m}{\rho}\\\Rightarrow \frac{4}{3}\pi r^3= \frac{m}{\rho}\\\Rightarrow r =\sqrt[3]{ {\frac{3m}{4\pi \rho}}}$

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

$r=\sqrt[3]{\frac{3\times 50g}{4\pi 9g/cm^3}} =1.33 cm$