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 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 • 523.6
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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