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Can someone please explain to me where 0.5642 came from?
A=πr²
A/π =πr²/π
A/π=r²
√A/π=√r²
√A/π=r
r=√A/π = 0.5642√A

Sagot :

Sqdancefanidn

Answer:

  0.5642 ≈ 1/√π

Step-by-step explanation:

You want to know where the coefficient 0.5642 comes from in ...

  r = 0.5642√A

Radius

Given the area formula for a circle, it can be rearranged to give the circle's radius in terms of its area.

  [tex]A=\pi r^2\\\\r^2=\dfrac{A}{\pi}\\\\\\r=\sqrt{\dfrac{A}{\pi}}=\dfrac{\sqrt{A}}{\sqrt{\pi}}\\\\\\r=\left(\dfrac{1}{\sqrt{\pi}\right)}\sqrt{A}=\dfrac{1}{\sqrt{3.14159\dots}}\sqrt{A}=\dfrac{1}{1.77245385\dots}\sqrt{A}\\\\\\r=(0.56418958\dots)\sqrt{A}\approx\boxed{0.5642\sqrt{A}}[/tex]

The value of the coefficient is 1/√π.

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Additional comment

When writing powers and roots in plain text, it is helpful to use parentheses to make it clear what the powers and roots are. The same is true for numerators and denominators.

  √A/π = (√A)/π ≠ √(A/π)

  2/3x = (2/3)x ≠ 2/(3x)

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