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Joe has exactly enough paint to paint the surface of a cube whose side length is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. If the volume of this sphere is \(\frac{K \sqrt{6}}{\sqrt{\pi}}\), then what is K?

 Feb 3, 2019
 #1
avatar+18293 
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Area of the cube =   2 x 2 *6 = 24 sq units  

 

VOLUME of a sphere = 4/3  pi r^3     find r from the volume equation given

4/3 pi r^3 = k sqrt 6 / sqrt pi

r^3 = 3/4  * k sqrt 6 /  pi sqrt pi

 

r = cubrt ( 3/4 *k sqrt 6/ (pi sqrt pi )

 

Surface of a sphere = 4 pi r^2     sub in the r value and equate to 24 sq units

 

4 pi (cubrt 3/4 *k sqrt 6/ (pi sqrt pi))^2 = 24

Solve fo k = 8

 Feb 3, 2019
edited by ElectricPavlov  Feb 3, 2019
edited by ElectricPavlov  Feb 3, 2019
 #3
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Thank you!

Lightning  Feb 3, 2019
 #2
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Surface area of a sphere =4*Pi*R^2
Surface area of a cube =S^2 x 6
2^2 x 6 =24 - SA of the cube.
24 = 4*Pi*R^2, solve for R
R = Sqrt(6/pi)
Volume of sphere =4/3 x Pi x [sqrt(6/pi)]^3
4/3 x Pi x [sqrt(6/pi)]^3 =K*sqrt(6) /sqrt(pi), solve for K
K = 8

 Feb 3, 2019
edited by Guest  Feb 3, 2019

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