Question

Calculus: A jumbo-size can of baked beans has a volume of 600cm^3. What dimensions will allow for the minimum amount of metal to produce the can?

Answer 1

this is a pain but a standard question. i am sure you can look it up and the answer is that the height should equal the diameter

Answer 2

maybe .sam will write it all out

Answer 3

\[600=\pi r^2 h\]
\[h=\frac{600}{\pi r^2}\]
\[A=2\pi r^2 +2\pi rh \]
\[A(r)=2\pi r^2 +2\pi r \times\frac{600}{\pi r^2}\]
\[A(r) =2\pi r^2 +\frac{1200}{r}\]
\[A'(r)=4\pi r -\frac{1200}{r^2}\] set equal zero and solve

Answer 4

@.Sam. look right?

Answer 5

\[V=\pi r^2 h\]
\[600=\pi r^2h\]
\[h=\frac{600}{\pi r^2}\]
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\[A=2\pi r(r+h)\]
\[A=2\pi r(r+\frac{600}{\pi r^2})\]
\[\frac{dA}{dr}=4\pi r-\frac{1200}{r^2}=0\]
\[r=300/\pi\]
=======================
\[h=\frac{600}{\pi r^2}\]
\[h=\frac{600}{\pi (300/\pi)^2}=\frac{1}{150}\pi\]

Answer 6

yep

Answer 7

nice picture !!

Answer 8

lol thanks