SOLUTION: If the diameter of a sphere is doubled, its surface becomes A. doubled the orginal surface B.four times the orginal surface C.eight times the orginal surface D. three times the

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Question 150914: If the diameter of a sphere is doubled, its surface becomes
A. doubled the orginal surface
B.four times the orginal surface
C.eight times the orginal surface
D. three times the orginal surface
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Surface area of a sphere: S=4pi%2Ar%5E2

Remember, the diameter is d=2r. So if the diameter is doubled, then the new radius is 2r units (instead of "r" units)


S=4pi%2Ar%5E2 Start with the given equation.


S=4pi%2A%282r%29%5E2 Replace the original "r" with "2r".


S=4pi%2A4r%5E2 Square 2r to get 4r%5E2



So the old equation is S%5Bold%5D=4pi%2Ar%5E2 and the new one is S%5Bnew%5D=4pi%2A4r%5E2


The ratio of the new surface area to the old surface area is then:

S%5Bnew%5D%2FS%5Bold%5D=%284pi%2A4r%5E2%29%2F%284pi%2Ar%5E2%29


Highlight the common terms


Cancel out the common terms


S%5Bnew%5D%2FS%5Bold%5D=4 Simplify


So the new surface area is simply 4 times the original surface area. So the answer is B