
Thomas E. answered 04/13/16
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Tom E., a Patient and Knowledgeable Mathematics Tutor for You
V = (Pi)r2h = 2000(Pi) Solve for h:
h = 2000(Pi)/(Pi)r2 = 2000r-2
The amount of material = 2(Pi)r2 + 2(Pi)rh substitute h from above
2(Pi)r2 + 2(Pi)(2000r-2)(r)=2(Pi)r2 +4000(Pi)r-1 Differentiate, set to zero and solve
4(Pi)r - 4000(Pi)r-2 = 0
r = 1000r-2
r3 = 1000
r = 10, h = 20