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Unformatted text preview: x =r and x = r . Again we start by computing ds . This time f ( x ) =x √ r 2x 2 So by the same algebra as in the previous example we get ds = r √ r 2x 2 dx Math 9C Fall 2011 (UCR) ProNotes November 13, 2011 4 / 1 So we now compute the surface area of the sphere with radius r as S = Z rr 2 π p r 2x 2 ds = Z rr 2 π p r 2x 2 r √ r 2x 2 dx = Z rr 4 π rdx = 4 π r 2 . Math 9C Fall 2011 (UCR) ProNotes November 13, 2011 5 / 1 It is interesting to notice the relationship between the volume of a sphere with raidus r which is V ( r ) = 4 / 3 π r 3 and the surface are of a sphere with radius r whcih is S ( r ) = 4 π r 2 . Do you see how the two are connected? Math 9C Fall 2011 (UCR) ProNotes November 13, 2011 6 / 1...
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