Wire is often sold in pounds spools according to the wire guage number. That number refers to the diameter of the wire. How many meters are in 3-Ib spool of 12 gauge aluminum wire? A 12-guage wire has a diameter of 0.0808 in. Aluminum has a density of 2.70 g/cm^3. (V=3.14r^2L)

Question

Wire is often sold in pounds spools according to the wire guage number. That number refers to the diameter of the wire. How many meters are in 3-Ib spool of 12 gauge aluminum wire? A 12-guage wire has a diameter of 0.0808 in. Aluminum has a density of 2.70 g/cm^3. (V=3.14r^2L)

Answer 1

I would change 0.0808 inches to cm and 3 pounds to grams. 2.54 cm = 1 inch and 453.6 g/lb, then 0.0808 in x (2.54 cm/in) = ?

and 3 pounds x (453.6 g/lb)= ?

The area of the wire is pi*r^2.

Volume = pi*r^2*length of wire
So if you know volume, pi, and r you can calculate length. Volume = mass/density = mass (grams)/density.
Solve for length in cm and convert to m

Answer 2

so i would 0.0808 in x (2.54 cm/in) = 2.6E-1

3 pounds x (453.6 g/lb)= 1.4E3
SO THAN WHAT DO I DO NEXT

Answer 3

0.0808 2.54 is not 0.26 and you shouldn't round to two places. You are allowed 3. My calculator reads about 0.205 cm. That's the diameter so take half of that to arrive at the radius. You've rounded 453.6 x 3 too much. I would keep it as 1360.8 grams. You can round later.

Next you calculate volume.
Volume = mass/density = 1360.8/2.70 = ?
Then V = pi*r^2*length
V from above.
pi = 3.14
r from above and square it.
Length. Solve for this.

Answer 4

To find the number of meters in a 3-lb spool of 12-gauge aluminum wire, we need to follow these steps:

Step 1: Convert the weight of the spool from pounds to grams.
Since 1 pound (lb) is approximately equal to 453.592 grams (g), we can calculate:
3 lb * 453.592 g/lb = 1360.776 g

Step 2: Calculate the volume of the wire in the spool.
We first need to find the radius of the wire. The gauge number refers to the diameter, so the radius (r) can be calculated by dividing the diameter by 2:
Diameter (d) = 0.0808 in
Radius (r) = 0.0808 in / 2 = 0.0404 in

We need to convert the radius from inches to centimeters since the density of aluminum is measured in g/cm^3:
1 in ≈ 2.54 cm
Radius (r) = 0.0404 in * 2.54 cm/in = 0.102616 cm

Using the formula for the volume of a cylinder:
Volume (V) = π * r^2 * L

We need the length (L) of the wire to calculate the volume. Unfortunately, the length is not provided in the question, so we cannot determine the volume or the number of meters in the spool without that information.

If you can provide the length of the wire, I can help you complete the calculation.