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A spherical ball fits snugly inside a cylindrical jar, so that the ball touches the top and bottom of the jar, and the sides of the jar.  The volume of the cylinder is $144 \pi.$  What is the total surface area of the cylinder?

 Jan 8, 2024
 #1
avatar+128448 
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Call the radius of the  sphere   = r  = the radius of the cylinder

 

Call the height of the  cylinder  =  2r  =  h

 

Volume of  cylinder  =   (4/3) pi r^3

 

144 pi  = (4/3) pi r^3

 

(3/4) 144 =  r^3

 

108   = r^3

 

(27 * 4)  = r^3

 

3(4)^(!/3)   =    r

 

Surface area of  cylinder  =  2 pi r^2  + 2pi r * h  =

 

2 pi [ 3(4)^(1/3)]^2  +  2 pi [( 3 )(4)^(1/3)] * [(2)  (3)(4)^(1/3) ]   ≈  427.48

 

cool cool cool

 Jan 9, 2024

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