Question

1. a sphere of mass 2 kg has a radius of 1.0 m. what is the density of the sphere in kg/m³. assume a sphere of radius r has a volume, $v=\frac{4}{3}pi r^{3}$. (a) 200 kg/m³ (b) $4pi$ kg/m³ (c) 0.238 kg/m³ (d) none of the above

Explanation:

Step1: Calculate the volume of the sphere

Given the volume formula for a sphere $V=\frac{4}{3}\pi r^{3}$, with $r = 1.0\ m$. Substitute $r$ into the formula:
$V=\frac{4}{3}\pi(1)^{3}=\frac{4}{3}\pi\ m^{3}$

Step2: Calculate the density of the sphere

The density formula is $
ho=\frac{m}{V}$, where $m = 2\ kg$ and $V=\frac{4}{3}\pi\ m^{3}$.
$
ho=\frac{2}{\frac{4}{3}\pi}=\frac{2\times3}{4\pi}=\frac{3}{2\pi}\approx0.477\ kg/m^{3}$

Answer:

(d) none of the above