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# The same amount of steel used to create eight solid steel balls

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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

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Nov 11, 2020