To find the mass of the cylindrical sample of magnesium, we can follow these steps:
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Calculate the volume of the cylinder using the formula for the volume of a cylinder: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
The radius \( r \) can be calculated from the diameter: \[ r = \frac{\text{diameter}}{2} = \frac{2 , \text{cm}}{2} = 1 , \text{cm} \]
Now, substituting the radius and height into the volume formula: \[ V = \pi (1 , \text{cm})^2 (8 , \text{cm}) = \pi (1) (8) = 8\pi , \text{cm}^3 \]
Using \( \pi \approx 3.14 \): \[ V \approx 8 \times 3.14 = 25.12 , \text{cm}^3 \]
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Calculate the mass of the cylinder using the formula: \[ \text{mass} = \text{density} \times \text{volume} \]
The given density of magnesium is \( 1.78 , \text{g/cm}^3 \).
Now, substituting the values into the mass formula: \[ \text{mass} \approx 1.78 , \text{g/cm}^3 \times 25.12 , \text{cm}^3 \approx 44.7856 , \text{g} \]
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Round the mass to the nearest hundredth: \[ \text{mass} \approx 44.79 , \text{g} \]
Therefore, the mass of the magnesium cylinder sample is approximately 44.79 grams.