+2499 \(V_{cylinder}= \pi r ^2 h \\ 300=\pi r^2h\\ h=\frac{300}{\pi r^2} \)
so let s put our h=300/(pi r^2) in \(S_{cylinder}=2 \pi rh+2 \pi r^2 \)
\(S_{cylinder}=2 \pi r( \frac{300}{\pi r^2 })+2 \pi r^2\\ S_{cylinder}=\frac{600}{r}+2 \pi r^2 \\ y=\frac{600}{x}+2\pi x^2 \text{ (so the minimum value of x is 3.628) }\)
https://www.desmos.com/calculator/mae20kmdjb
so r is 3.628 put it in term s of \(h=\frac{300}{\pi r^2}\)
\(h=\frac{300}{3.628^2 \pi} \\ h = 7.25499\\ S_{cylinder}=2 \times \pi \times 3.628 \times 7.25499+2\times\pi\times 3.628^2=248.0820699 \dots\)
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