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Joe has exactly enough paint to paint the surface of a cube whose main diagonal is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere.  Find the radius of the sphere.

 Nov 26, 2020
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If the main diagonal is 2......then  we  can find  the side, s   by

 

2  = sqrt  ( 3s^2)

 

2 = sqrt (3) s

 

s =  2/sqrt (3)

 

s^2  = 4/3

 

Surface area of this cube  is    6 s^2  =   6 (4/3)  =  24/3  =    8 units^2

 

And for the sphere radius :

 

8 =   4 pi r^2

 

r^2  =  8 / ( 4 pi)  =   2/ pi

 

r =  sqrt  (2/pi)  units

 

 

cool cool cool

 Nov 26, 2020

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