Respuesta :
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.
[tex]\boxed{ \ \rho = \frac{m}{V} \ } \rightarrow \boxed{ \ V = \frac{m}{\rho} \ }[/tex]
[tex]\boxed{ \ V = \frac{22 \ g}{8.96 \ g/cm^3} \ }[/tex]
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.
[tex]\boxed{ \ d = 0.25 \ mm = 0.025 \ cm \ }[/tex]
The formula of the cylinder volume is [tex]\boxed{ \ Volume = Area \ of \ the \ base \times Length \ }[/tex]
[tex]\boxed{ \ Volume = \frac{1}{4} \pi d^2 \times Length \ }[/tex]
[tex]\boxed{ \ 2.455 = \frac{1}{4} \pi (0.025)^2 \times Length \ }[/tex]
[tex]\boxed{ \ 2.455 = 4.91 \times 10^{-4} \times Length \ }[/tex]
[tex]\boxed{ \ Length = \frac{2.455}{4.91 \times 10^{-4}} \ }[/tex]
[tex]\boxed{ \ Length = \frac{2.455 \times 10^4}{4.91} \ }[/tex]
[tex]\boxed{\boxed{ \ Length = 5,000 \ cm = 50 \ m \ }}[/tex]
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
[tex]\boxed{\boxed{ \ density = \frac{massa}{volume} \ }}[/tex]
with the symbol as follows
[tex]\boxed{\boxed{ \ \rho = \frac{m}{V} \ }}[/tex]
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 https://brainly.com/question/4053884
- The theoretical density of platinum which has the FCC crystal structure. https://brainly.com/question/5048216
- Determine the density of our sun at the end of its lifetime https://brainly.com/question/5189537
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
