Micrometer reading/area of wire calculation

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SUMMARY

The discussion centers on calculating the cross-sectional area of a wire with a measured diameter of 0.30 mm. The correct formula for the area is confirmed as Πr², where r is half the diameter. The calculation yields a cross-sectional area of 7.0 x 10⁻⁸ m², which should be expressed in square millimeters for consistency with the diameter measurement. Participants clarify the importance of unit consistency in calculations.

PREREQUISITES
  • Understanding of basic geometry, specifically the formula for the area of a circle
  • Familiarity with metric units, particularly millimeters and square millimeters
  • Knowledge of scientific notation and its application in calculations
  • Ability to interpret measurement units accurately
NEXT STEPS
  • Review the formula for the area of a circle and its applications in engineering
  • Learn about unit conversions between different metric measurements
  • Explore scientific notation and its use in expressing small values
  • Investigate common applications of wire cross-sectional area in electrical engineering
USEFUL FOR

Students in engineering, electricians, and anyone involved in wire sizing or electrical applications will benefit from this discussion.

Deliria
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I measured the diameter of a wire and got 0.30. This is in millimeters right?

How would you calculate the cross sectional area? Is it just Πr²?

so Π x (0.15x10⁻³ x 0.15x10⁻³)
= 7.0 x 10⁻⁸m²

Is this right?
 
Last edited:
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Well, it could be 0.30 mm, but without further information it could just as easily be for instance 0.30 cm.

Assuming that the wire has a circular cross-section, then yes, your approach is right.
 
Deliria said:
I measured the diameter of a wire and got 0.30. This is in millimeters right?

How would you calculate the cross sectional area? Is it just Πr²?

so Π x (0.15x10⁻³ x 0.15x10⁻³)
What is the exponent on 10 below? It looks like an accent mark, not a number.
Also, since your units are mm for the wire diameter, I think, why not leave the cross-section area in sq. mm.?
Deliria said:
= 7.0 x 10⁻⁸m²

Is this right?
 
Last edited:
Thanks for the help guys! :)

I'm pretty sure the diameter was in millimeters.

Mark44 said:
What is the exponent on 10 below? It looks like an accent mark, not a number.
Also, since your units are cm for the wire diameter, I think, why not leave the cross-section area in sq. cm.?

In my final answer? 8

I couldn't fit it all in the answer box, lol. Standard form was the only way :(
 
Yeah, I meant mm, not cm. I edited these units in my previous post.
 

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