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The same amount of steel used to create eight solid steel balls, each with a radius of 5 inches, is used to create one larger steel ball. What is the radius of the larger ball?

 

 Nov 10, 2020
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The same amount of steel used to create eight solid steel balls, each with a radius of 5 inches, is used to create one larger steel ball. What is the radius of the larger ball?    

 

The volume of 1 ball                V  =  4/3 • π • r3  

                                                V  =  4/3 • 3.1416 • 53  

                                                V  =  4/3 • 3.1416 • 125  

                                                V  =  523.6   

 

The volume of 8 balls               V  =  8 • 523.

                                                 V  =  4,188.8      This equals the volume of the big ball  

 

Using the same formula for the volume of a sphere, 

work backwards to get the value of "r"  

 

                                                  V  =  4/3 • π • r3  

                                                  4,188.8  =  4/3 • 3.1416 • r3  

                                                  4,188.8  =  4.1888 • r3          Okay, right here, when I saw where this was going,  

                                                                                                I went back and checked all my numbers.  I can't  

                                                                                                find any mistake.  So, keeping on keeping on....   

Divide both sides by 4.1888       4,188.8/4.1888  =  r3                                        

                                                   1,000  =  r3  

 

Take the cube root of both sides      r  =  10       This is the radius of the big ball  

.

 Nov 11, 2020

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