What length of a cylindrical piece of tungsten wire having a radius of 2.11 mm has a mass of 66.6 g? The density of tungsten is 19.25 g/cm³. A)2.47× 10^-3 m B)1.79 × 10² m C)2.47 × 10^-1 m D)4.04 × 10^-2 m E)4.04 × 10^-4 m

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Quizplus · Accepted Answer

To find the length of the tungsten wire, we use the formula for the volume of a cylinder $V = \pi r^2 h$ and the relationship between mass, volume, and density $m = \rho V$. Given the mass $m = 66.6 \, \text{g}$, density $\rho = 19.25 \, \text{g/cm}^3$, and radius $r = 2.11 \, \text{mm} = 0.211 \, \text{cm}$, we can solve for the height (length) $h$. Rearranging the formula gives $h = \frac{m}{\pi r^2 \rho}$. Substituting the given values and solving for $h$ gives a length in centimeters, which can be converted to meters, resulting in an answer that matches option C, $2.47 \times 10^{-1} \, \text{m}$.

What Length of a Cylindrical Piece of Tungsten Wire Having