Calculate Circle Radius/Diameter from Surface Area

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Discussion Overview

The discussion revolves around calculating the radius and diameter of a circle from its surface area. Participants explore the mathematical relationships involved, clarify terminology, and seek examples to illustrate the calculations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant questions how circular surface area values are square rooted and seeks a formula to derive the radius or diameter from a given surface area.
  • Another participant provides the formula for radius as \( r = \sqrt{\frac{S}{\pi}} \) derived from the area formula \( S = \pi r^2 \).
  • A participant expresses confusion regarding the application of the formula, noting discrepancies in calculated values for a circle with a specified diameter.
  • Clarifications are made regarding the terminology of "surface area" versus "area" in the context of two-dimensional circles.
  • One participant reiterates the correct formula for radius and emphasizes the need for proper units in calculations.

Areas of Agreement / Disagreement

Participants generally agree on the formula for calculating the radius from the area, but there are discrepancies in the application of the formula and the resulting values, indicating unresolved confusion.

Contextual Notes

There are limitations in the clarity of the examples provided, and some participants express uncertainty about the calculations and terminology used.

magmash
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Hi

How is circular surface area values square rooted ??. I am using this formula r2Xπ=mm2 to calculate the surface area of a circle but i want to know if there is a formula to get back to the diameter or the radius of the circle ?.

example i have a circular surface area of 5.26mm2 and i want the diameter of that value, how do i solve this ?

Thanks in advance
 
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S=\pi r^2 \Rightarrow r^2=\frac{S}{\pi} \Rightarrow r=\sqrt{\frac{S}{\pi}}
 
Shyan said:
S=\pi r^2 \Rightarrow r^2=\frac{S}{\pi} \Rightarrow r=\sqrt{\frac{S}{\pi}}
Thanks for the replay Shyan.

a circel with a diameter of 1.29mm 0.6452π = 1.30 The formula you mentioned √s/π gives a value of 0.362.. ?

Could you show me an example, I would be very thanks full
 
magmash said:
Thanks for the replay Shyan.

a circel with a diameter of 1.29mm 0.6452π = 1.30 The formula you mentioned √s/π gives a value of 0.362.. ?

Could you show me an example, I would be very thanks full
Careful boy! Its not r=\frac{\sqrt{S}}{\pi}, its r=\sqrt{\frac{S}{\pi}}.
 
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:DThanks
 
magmash said:
Hi

How is circular surface area values square rooted ??.
We don't call it "surface area" - just area. Surface area applies to surfaces in three dimensions. For objects in the plane (two dimensions), we talk about the area.
magmash said:
I am using this formula r2Xπ=mm2
The actual formula is ##A = \pi r^2##. If r is given in mm., then the units of area will be square millimeters or mm2. The formula shouldn't explicitly show units.
magmash said:
to calculate the surface area of a circle but i want to know if there is a formula to get back to the diameter or the radius of the circle ?.
From the equation ##A = \pi r^2##, to get the radius, solve for r. To do this, divide both sides of the equation by ##\pi##, then take the square root. Once you have the radius r, you can get the diameter using d = 2r.
magmash said:
example i have a circular surface area of 5.26mm2 and i want the diameter of that value, how do i solve this ?

Thanks in advance
 

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