Chemistry, 08.12.2019 17:31 DiamNeli

Acopper wire (density=8.96g/cm3) has a diameter of 0.25 mm. if a sample of this copper wire has a mass of 22g, how long is the wire ?

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Answer from: bellsbella34

5,000 cm (or 50 m) long.

Further explanation

Given:

A copper wire has a diameter of 0.25 mm.A sample of this copper wire has a mass of 22 g.Density of copper (ρ) = 8.96 g/cm³

Question:

How long is the wire?

Problem-solving:

Step-1: finding the volume (V) in cm³ of 22 g copper wire.

The formula can be rearranged to calculate the volume of an object.

$\boxed{ \ \rho = \frac{m}{V} \ } \rightarrow \boxed{ \ V = \frac{m}{\rho} \ }$

$\boxed{ \ V = \frac{22 \ g}{8.96 \ g/cm^3} \ }$

If all other units are crossed out, generating the desired unit is grams, that means the problem is set in the correct dimensions

Hence, the volume of 22 g copper wire is 2.455 cm³.

Step-2: finding the length of the wire

Let us prepare the base diameter in cm.

$\boxed{ \ d = 0.25 \ mm = 0.025 \ cm \ }$

The formula of the cylinder volume is $\boxed{ \ Volume = Area \ of \ the \ base \times Length \ }$

$\boxed{ \ Volume = \frac{1}{4} \pi d^2 \times Length \ }$

$\boxed{ \ 2.455 = \frac{1}{4} \pi (0.025)^2 \times Length \ }$

$\boxed{ \ 2.455 = 4.91 \times 10^{-4} \times Length \ }$

$\boxed{ \ Length = \frac{2.455}{4.91 \times 10^{-4}} \ }$

$\boxed{ \ Length = \frac{2.455 \times 10^4}{4.91} \ }$

$\boxed{\boxed{ \ Length = 5,000 \ cm = 50 \ m \ }}$

Thus, the copper wire has 5,000 cm (or 50 m) long.

Notes:

In Greek letters, the density is expressed in letters ρ (read: rho) and is defined as the mass of the substance divided by its volume. The formula that states the relationship between them is

$\boxed{\boxed{ \ density = \frac{massa}{volume} \ }}$

with the symbol as follows

$\boxed{\boxed{ \ \rho = \frac{m}{V} \ }}$

Based on the formula, the standar units of density are kg/m³ or g/cm³.

Objects with identical types will allow the same density. Therefore it can be noted that density is one of the characteristics of a substance because it provides a specified value.

Note that density is

always constant can be used as a conversion factor can be used to identify an unknown hypothetical substance varies from element to element and substance to substance can be measured for all substances, solids, liquids, and gases.

How tight or heavy an object can be observed by comparing its density.

Learn more About the mass and density of substances linkThe theoretical density of platinum which has the FCC crystal structure. linkDetermine the density of our sun at the end of its lifetime link

Keywords: a copper wire, a diameter of 0.25 mm, density = 8.96 g/cm³, a sample, a mass of 22 g, how long is the wire? volume of cylinder, area of the base, length

Answer from: Quest

mark him as !

Answer from: Quest

The correct answer is d