- #1
EricPowell
- 26
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Homework Statement
An open-topped cylinder is to have a volume of 250 cm3. The material for the bottom of the pot costs 4 cents per cm2, and the material for the side of the pot costs 2 cents per cm2. What dimensions will minimize the total cost of this pot?
The Attempt at a Solution
$$
A_{bottom}=πr^2
\\
C_{bottom}=4(πr^2)
$$
$$
A_{side}=2πrh
\\
C_{side}=2(2πrh)
$$
$$
V=πr^2h
\\
250=πr^2h
\\
h=\frac {250}{πr^2}
\\
∴C_{side}=2(2πr\frac {250}{πr^2})
$$
$$
C_{total}=4(πr^2+2(2πr\frac {250}{πr^2})
\\
\frac {d(C_{total})}{d(r)}=8πr-\frac{1000}{πr^3}
$$
Then I tried to use the first derivative test. I am stuck.
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