Page 110 - How To Solve Word Problems In Calculus

Substituting into the equation for S obtained in step 2, we
obtain S as a function of r.

2000
S(r) = 2πr + 2πr 2
πr 2
4000
S(r) = + 2πr 2 0 < r < ∞
r

Step4
S(r) = 4000r −1 + 2πr 2

S (r) =−4000r −2 + 4πr
4000
0 =− + 4πr
r 2
4000
= 4πr
r 2

3
4πr = 4000
1000
3
r =
π
10
r = √ in
3 π

2000
Since h = , the corresponding height is
πr 2
2000 2000 2000 20
h = = = = √ in
2 100 1/3 3
10 100π π
π √ π 2/3
3 π π
Step5

S (r) = 8000r −3 + 4π
8000
= + 4π
r 3
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