To find the mass of the magnesium cylinder, we first need to calculate its volume using the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height.
Given:
- The height \(h = 8\) cm,
- The diameter is \(2\) cm, so the radius \(r = \frac{2}{2} = 1\) cm.
Now, substituting the values into the formula:
\[ V = \pi (1)^2 (8) = \pi (1)(8) = 8\pi \]
Using \(\pi \approx 3.14\):
\[ V \approx 8 \times 3.14 = 25.12 , \text{cm}^3 \]
Next, we can find the mass using the density formula:
\[ \text{mass} = \text{density} \times \text{volume} \]
Given the density of magnesium is \(1.78 , \text{g/cm}^3\):
\[ \text{mass} = 1.78 , \text{g/cm}^3 \times 25.12 , \text{cm}^3 \]
Calculating the mass:
\[ \text{mass} \approx 1.78 \times 25.12 \approx 44.7496 , \text{g} \]
Rounding to the nearest hundredth:
\[ \text{mass} \approx 44.75 , \text{g} \]
Thus, the mass of the magnesium cylinder sample is approximately 44.75 g.