Question 1203180
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The formula for the surface area of a sphere, and the units you use in your calculations, are irrelevant to the problem.<br>
Surely the intent of the problem is to help you learn a very powerful general geometric principle:<br>
If the scale factor (ratio of linear measurements) between similar figures is A:B, then the ratio of area measurements in the two figures is A^2:B^2, and the ratio of volume measurements in the two figures is A^3:B^3.<br>
In this problem, your are given that the ratio of surface areas of two spheres is 2:1.  In terms of the geomtric principle, that is the "A^2:B^2; and in the problem we are supposed to determine the ratio of linear measurements, which is the "A:B".<br>
Since the ratio of surface areas in the two similar figures is 2:1, the ratio of the diameters (linear measurements) is {{{sqrt(2):sqrt(1)=sqrt(2):1}}}.<br>
ANSWER: the diameter must be altered by a factor of {{{sqrt(2)}}}.<br>