What length of a cylindrical piece of tungsten wire having a radius of 2.27 mm has a mass of 10.0 g? The density of tungsten is 19.25 g/cm³ and Volume = πr²h. A) 3.21 × 10^-4 m B) 3.12 × 10¹ m C) 3.21 × 10^-2 m D) 3.12 × 10^-1 m E) 3.12 × 10^-3 m

Question

Quizplus · Accepted Answer

Using the formula for the volume of a cylinder, we have:

Volume = πr2h

We are given the radius (r = 2.27 mm) and the mass (m = 10.0 g), and we know the density (ρ=19.25 g/cm³). We can use the density to find the volume:

ρ = m/V => V = m/ρ = 10.0 g / 19.25 g/cm³ = 0.5195 cm³

Now we can solve for the height (h):

V = πr2h => h = V / (πr2) = 0.5195 cm³ / (π x (2.27 mm)² x 1 cm²/100 mm² ) = 0.321 cm or 3.21 x 10⁻² m

Therefore, the length of the wire is 3.21 x 10⁻² m or 3.21 x 10⁻² x 10⁻² = 3.21 x 10⁻⁴ m = 3.21 x 10⁻² cm. Choice C is the closest option.

What Length of a Cylindrical Piece of Tungsten Wire Having