# SOLUTION: Suppose you wish to reduce the volume of a sphere by a factor of 7.00. If it's original radius was R, what is the reduced radius in terms of R? By what factor does the sphere's sur

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 Click here to see ALL problems on Volume Question 262877: Suppose you wish to reduce the volume of a sphere by a factor of 7.00. If it's original radius was R, what is the reduced radius in terms of R? By what factor does the sphere's surface area change? I have no idea how to even approach this. I'm assuming that the answers to both the questions will have 7's in them.Answer by josmiceli(9668)   (Show Source): You can put this solution on YOUR website!The formula for the volume of a sphere is (1) Making the sphere seven times smaller means multiplying by Let = the new radius when is of what it used to be (2) Now I need to find in terms of Multiply both sides of (1) by (2) (2) Now I need to substitute in (1) for in (2) (2) (2) Now take the cube root of both sides (2) is the reduced radius in terms of The surface areas are proportional to and Because so I can rewrite (2) as (2) (2) Now square both sides This is the factor that the surface area changes by