SOLUTION: The surface of a sphere is 86 pie ft^2? what is the diameter of the sphere?

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Question 61384This question is from textbook An Incremental Development
: The surface of a sphere is 86 pie ft^2? what is the diameter of the sphere? This question is from textbook An Incremental Development

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
The surface of a sphere is 86 pie ft^2? what is the diameter of the sphere?
The formula for the surface area of a sphere is highlight%28S=4%2Api%2Ar%5E2%29
S=86%2Api ft^2
86%2Api=4%2Api%2Ar%5E2
86%2Api%2F%284%2Api%29=4%2Api%2Ar%5E2%2F%284%2Api%29
21.5=r%5E2
sqrt%2821.5%29=sqrt%28r%5E2%29
4.636809248=r
Diameter = 2*radius
d=2%284.6268091248%29
d=9.2736 ft
:
You can substitute r=d/2 into the formula and reduce your formula:
S=4%2Api%2A%28d%2F2%29%5E2
S=4%2Api%2A%28d%5E2%2F4%29
S=4%2Api%2Ad%5E2%2F4
S=pi%2Ad%5E2
substitute S=86%2Api into the formula and solve for d.
86%2Api=pi%2Ad%5E2
86%2Api%2F%28pi%29=pi%2Ad%5E2%2F%28pi%29
86=d%5E2
sqrt%2886%29=sqrt%28d%5E2%29
sqrt%2886%29=d
d=sqrt%2886%29ft
That's as pretty as I can make it. If you put that in your calculator, you'll see it's the same answer.
Happy Calculating