If the volume of a sphere doubles, what is the ratio of the surface area of the new, larger sphere to the old?

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chicka152m0w3 · Accepted Answer

Let&#039;s begin with two formulas for a sphere&#039;s surface area       S   and volume       V  , assuming that the sphere&#039;s radius is       R  :      S    =    4    π          R      2            V    =          4      3        π          R      3      To double the volume, we have to increase the radius by multiplying it by                     2                    3            Indeed, let             R      1        =    R                  2                    3            Then the volume of a sphere with radius             R      1       will be            V      1        =          4      3        π                  R        1        3              =          4      3        π                  (        R                              2                                3                          )            3        =          8      3        π          R      3       - twice larger than original volume.With radius             R      1        =    R                  2                    3             the surface area of a new sphere will be      4    π                  R        1        2              =    4    π          R      2                      (                              2                                3                          )            2        =    4                  4                    3              π          R      2      the old surface area to the new surface area ratio is equal to                    4                              4                                3                          π                  R          2                            4        π                  R          2                      =                  4                    3

If the volume of a sphere doubles, what is the ratio of the surface area of the new, larger sphere to the old?

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