To find the mass of the cylindrical piece of magnesium, we can follow these steps:
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Calculate the volume of the cylinder using the formula: \[ \text{Volume} = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
Given:
- Height (h) = 8 cm
- Diameter = 2 cm, so radius (r) = diameter / 2 = 1 cm
Substituting the values into the volume formula: \[ \text{Volume} = \pi (1 \text{ cm})^2 (8 \text{ cm}) = \pi (1)(8) = 8\pi \text{ cm}^3 \] Using \( \pi \approx 3.14 \): \[ \text{Volume} \approx 8 \times 3.14 = 25.12 \text{ cm}^3 \]
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Calculate the mass using the density formula: \[ \text{Mass} = \text{Density} \times \text{Volume} \] Given the density of magnesium is \( 1.78 \text{ g/cm}^3 \): \[ \text{Mass} = 1.78 \text{ g/cm}^3 \times 25.12 \text{ cm}^3 \] \[ \text{Mass} \approx 44.7486 \text{ g} \]
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Round the mass to the nearest hundredth: Rounding \( 44.7486 \) gives \( 44.75 \).
Thus, the mass of the cylindrical sample of magnesium is approximately 44.75 g.