28 pure silver has a density of 10.5 g/cm³. samantha has a pure silver charm on her necklace in the shape of…

Explanation:

Step1: Calculate the volume of the sphere

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$. Given $r = 0.5$ cm, we substitute $r$ into the formula: $V=\frac{4}{3}\pi(0.5)^{3}=\frac{4}{3}\pi\times0.125=\frac{\pi}{6}\text{ cm}^3$.

Step2: Calculate the mass using density - mass - volume relationship

The density formula is $\rho=\frac{m}{V}$, where $\rho = 10.5$ g/cm³ and $V=\frac{\pi}{6}\text{ cm}^3$. Rearranging for $m$ gives $m=\rho V$. Substituting the values, we get $m = 10.5\times\frac{\pi}{6}=\frac{10.5\pi}{6}\approx\frac{10.5\times3.14}{6}=\frac{32.97}{6}= 5.495$ g.

Step3: Round the mass to the nearest tenth

Rounding $5.495$ g to the nearest tenth gives $5.5$ g.

Answer:

$5.5$ g