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A circle is revolved about a diameter and the sphere obtained has numerically the same volume as the circle had area.  Find the circumference of the circle.

 May 20, 2020
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A circle is revolved about a diameter and the sphere obtained has numerically the same volume as the circle had area.  Find the circumference of the circle.

 

 

The formulas for area and for volume both use the radius, so let's find that first, and then figure the circumference. 

 

V  =  (4/3) (π) r3  

 

A  =  (π) r2  

 

Set them equal                                (4/3) (π) r3  =  (π) r2  

 

Divide both sides by (π) r2               (4/3) r  =  1 

 

Divide both sides by 4/3                    r  =  3/4   

 

Circumference is 2 π r                       C  =  2 π  r   =  2 x 3.1416 x 3/4  =  3.1416 x 3/2  =  about 4.7  

 

  

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 May 20, 2020

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