If a sphere's surface area is doubled, what is the corresponding change in radius?

The radius has an increase of 41.4%

Step-by-step explanation:

We have that the surface area formula is equal to:

a = 4 * pi * r ^ 2

in this case if you assume an area of 100 and we calculate the radius it would be:

100 = 4 * pi * r ^ 2

we solve for r:

r ^ 2 = 100/4 * pi

r ^ 2 = 100 / (4 * 3.14)

r ^ 2 = 7.9617

r = 2,822

now if we double the area, that is 200:

r ^ 2 = 200 / (4 * 3.14)

r ^ 2 = 15.9236

r = 3,990

So the change of the radius would be:

3.99 / 2,822 = 1,414

That is to say that the radius has an increase of 41.4%