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Hi I was hoping for some help on this 3 step problem:
a) Given Surface area of sphere, A = 4*pi*r^2 and Volume = 4/3*pi* r^3, solve for V in terms of A.
b) Find dV/dA.
c) The volume of a ball of radius 4in is increased by .5 in^3. Estimate the increase in the
area.
I get stuck at part c...
a) I solved for r in area formula and substituted in the volume formula to get:
V= A/3* sqrt(A/4*pi)
b) dV/dA = Sqrt(x)/4*sqrt(pi) *thanks to wolfram alpha
c) My first thought was to find volume of a ball with radius 4, add .5 then solve for the new radius. Then plug that into the surface area formula and see what I get. However I feel there must be another way using part A and B.
Any help is appreciated. Thanks.