Question

A sphere of radius $r$ has a mass $m$. Its density is .

• A. $\frac{4{\mathrm{\pi r}}^3}{3}$
• B. $\frac{3m}{4{\mathrm{\pi r}}^3}$
• C. $\frac{4{\mathrm{\pi r}}^3}{3m}$

Answer 1

The correct option is B $\frac{3m}{4{\mathrm{\pi r}}^3}$

Given:
Mass of the sphere: $m$
Radius of the sphere: $r$

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

From definition of density:
$\rho =\frac{m}{V}$
$\rho =\frac{3m}{4\pi r^3}$