To find the mass of the magnesium cylinder, we first need to calculate its volume and then use the density to find the mass.
Step 1: Calculate the volume of the cylinder
The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder
Given:
- The diameter of the cylinder is 2 cm, so the radius \( r \) is half of that:
\[ r = \frac{2 , \text{cm}}{2} = 1 , \text{cm} \]
- The height \( h \) is 8 cm.
Now we can calculate the volume:
\[ V = \pi (1 , \text{cm})^2 (8 , \text{cm}) = \pi (1) (8) = 8\pi , \text{cm}^3 \]
Using \( \pi \approx 3.14 \):
\[ V \approx 8 \times 3.14 = 25.12 , \text{cm}^3 \]
Step 2: Calculate the mass using density
The formula for mass \( m \) is:
\[ m = \text{density} \times V \]
Given the density of magnesium is \( 1.78 , \text{g/cm}^3 \):
\[ m = 1.78 , \text{g/cm}^3 \times 25.12 , \text{cm}^3 \]
Calculating the mass:
\[ m \approx 1.78 \times 25.12 \approx 44.71 , \text{g} \]
Final Answer
The mass of the magnesium cylinder sample is approximately 44.71 g when rounded to the nearest hundredth.