a piece of magnesium has a cylindrical shape with a height of 8 centimeters and a diameter of 2 centimeters…

Explanation:

Step1: Calculate cylinder radius

Radius $r=\frac{d}{2}=\frac{2}{2}=1$ cm

Step2: Calculate cylinder volume

Volume $V = \pi r^{2}h$, substituting $r = 1$ cm, $h = 8$ cm and $\pi\approx3.14$, we get $V=3.14\times1^{2}\times8=25.12$ $cm^{3}$

Step3: Calculate mass using density - mass - volume relation

We know $\rho=\frac{m}{V}$, so $m=\rho V$. Given $\rho = 1.78$ g/$cm^{3}$ and $V = 25.12$ $cm^{3}$, then $m=1.78\times25.12 = 44.7136$ g

Step4: Round the result

Rounding $44.7136$ g to the nearest hundredth gives $44.71$ g

Answer:

$44.71$ g