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

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) (Show Source): You can put this solution on YOUR website!
Surface area of a sphere:

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

Start with the given equation.

Replace the original "r" with "2r".

Square 2r to get

So the old equation is and the new one is

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

Highlight the common terms

Cancel out the common terms

Simplify

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