Flashcards: How to find volume of a region

Suppose I want to construct a cylindrical container. It costs 5 dollars per square foot to construct the two circular ends and 2 dollars per square foot for the rounded side. If I have a budget of 100 dollars, what's the maximum volume possible for this container?

\frac{70}{3}\sqrt{\frac{\pi}{3}}\displaystyle \frac{70}{3}\sqrt{\frac{\pi}{3}}

\frac{70}{6}\sqrt{33\pi}\displaystyle \frac{70}{6}\sqrt{33\pi}

V=\frac{50}{3}\sqrt{\frac{10}{3\pi}}\displaystyle V=\frac{50}{3}\sqrt{\frac{10}{3\pi}}

\sqrt{\frac{10\pi}{3}}\displaystyle \sqrt{\frac{10\pi}{3}}

\frac{15}{2}\sqrt{\frac{10\pi}{3}}\displaystyle \frac{15}{2}\sqrt{\frac{10\pi}{3}}

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