Geometry

 

What is the radius of the sphere whose volume is 33 times its surface area?    

 

                                            V_sphere  =  (4 / 3) π r³    

                                            A_sphere  =  4 π r²    

 

                                                       V  =  33A    

 

                                          (4 / 3) π r³  =  33 • 4 π r²         

 

multiply both sides by 3             4 π r³  =  396 π r²     

 

divide both sides by π r²                  4r  =  396            

 

                                                           r  =  99    

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