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A hemisphere-shaped bowl with radius 1 foot is filled full with chocolate. All of the chocolate is then evenly distributed between 64 congruent, smaller hemisphere-shaped molds. What is the radius of each of the smaller molds, in feet?

 Nov 26, 2020
 #1
avatar+116126 
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V (hemisphere )   =  (2/3)pi * (1)^3  =   2pi/3   ft^3

 

One  of  the smaller hemispheres contains    (2pi/3) / 64 =  (2/192) pi    =  pi/96  ft^3  of chocolate

 

pi/96  = (2/3) pi * r^3

 

1/96  = (2/3) r^3

 

(1/96) (3/2)  = r^3

 

(3/192)  = r^3

 

(1/64)  = r^3        take the cube root of both sides

 

(1/4) ft  =  r 

 

 

cool cool cool

 Nov 26, 2020
edited by CPhill  Nov 27, 2020
 #2
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Chris, the cube root of 64 is 4....  

Guest Nov 26, 2020
 #3
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Sorry....correction made   !!!

 

 

cool cool cool

CPhill  Nov 27, 2020

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