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20 December, 14:27

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

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  1. 20 December, 16:16
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    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%
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