Page 138 - How To Solve Word Problems In Calculus

2000
= 4πr
r 2
3
4πr = 2000
500
3
r =
π

3 500 3 4
r = = 5
π π
The corresponding value of h is
1000 1000 1000
h = =
=
πr 2 3 4 2 4 2/3
π 5 25π 2/3
π π

1/3
40 10 · 4 3 4
= = = 10
π 1/3 2/3 π 1/3 π
4
We test the critical value using the second derivative test (optional).
S (r ) = 4000r −3 + 4π

4000
= + 4π
r 3
Since the critical value is positive (its exact value is not needed), S

4
is certainly positive at 5 3 ,so S(r ) has a relative minimum here.
π
Since it is the only relative extremum on the interval (0, ∞)itisthe
location of the absolute minimum.
16.
r

2r
h

2r

The material used in the construction of the can consists of three
pieces. The area of the body of the can is 2πrh and the material
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