# Question e406e

Jul 25, 2015

I found: $m a s s = 1 \times {10}^{-} 3 k g$

#### Explanation:

Considering it as a cylindrical wire you can evaluate its volume $V$ as:
$V = \pi {r}^{2} \times h = 3.14 {\left(\frac{0.002}{2}\right)}^{2} \times 0.32 = 1 \times {10}^{-} 6 {m}^{3}$
From:
$\mathrm{de} n i s i t y = \frac{m a s s}{v o l u m e}$
$m a s s = \mathrm{de} n s i t y \times v o l u m e = 1000 \times 1 \times {10}^{-} 6 = 1 \times {10}^{-} 3 k g$

Jul 25, 2015

Mass of the wire: 1 g

#### Explanation:

Density is defined as mass per unit of volume.

In your case, the density of the wire is known to be equal to ${\text{1000 kg/m}}^{3}$, which means that ${\text{1 m}}^{3}$ of volume will have a mass of $\text{1000 kg}$.

So, in order to determine the mass of the wire, you need to know what volume it occupies. You can assume it to have the shape of a very long and thin cylinder, so that tis volume can be determine by using

$V = \pi \cdot {r}^{2} \cdot h$, where

$r$ - the radius of the wire;
$h$ - its length.

In your case, the wire hs a diameter of 0.002 m, which means that its radius will be

$r = \frac{d}{2} = \text{0.002 m"/2 = "0.001 m}$

The wire's volume will thus be

V = pi * ("0.001 m")^2 * "0.32 m" = 1.0 * 10^(-6)"m"^3

This means that the mass of the wire will be

1.0 * 10^(-6)cancel("m"^3) * "1000 kg"/(1cancel("m"^3)) = 1.0 * 10^(-3)"kg"#

Expressed in grams and rounded to one sig fig, the number of sig figs you gave for the diameter of the wire, the answer will be

$1.0 \cdot {10}^{- 3} \cancel{\text{kg") * (10^3"g")/(1cancel("kg")) = color(green)("1 g}}$

Jul 25, 2015

1 gram (CGS) or ${10}^{-} 3$ Kg (SI)

#### Explanation:

assuming the wire is cylindrical:

Area of the cross section: $\pi \cdot {r}^{2}$= $3.14 \cdot {\left(\frac{0.002}{2}\right)}^{2} = 3.14 \cdot 0.000001 = 3.14 \cdot {10}^{- 6} {m}^{2}$

Total volume=area x length: $3.14 \cdot {10}^{-} 6 \cdot 0.32 = 1 \cdot {10}^{-} 6 {m}^{3}$

Total mass=volume x density: $1 \cdot {10}^{-} 6 {m}^{3} \cdot 1000 \frac{K g}{{m}^{3}} = {10}^{-} 3 K g = 1 g$

The numbers were chosen to make the math very simple. The total mass is 1 gram.

Incidentally, this wire is made of a material with the same density as water (real metals are much denser).