Question

a cylinder with radius r and height h has volume 1 and tsa 12 find 1/r+1/h

Answer 1

Dear Student

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{cylinder}=1\mathrm{cubic}\mathrm{units} \\ \Rightarrow {\mathrm{\pi r}}^2\mathrm{h}=1...\left(1\right) \\ \mathrm{TSA}\mathrm{of}\mathrm{cylinder}=12\mathrm{square}\mathrm{units} \\ \Rightarrow 2\mathrm{\pi rh}+2{\mathrm{\pi r}}^2=12 \\ \Rightarrow \mathrm{\pi rh}+{\mathrm{\pi r}}^2=6 \\ \mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}{\mathrm{\pi r}}^2\mathrm{h},\mathrm{we}\mathrm{get} \\ \frac{\mathrm{\pi rh}}{{\mathrm{\pi r}}^2\mathrm{h}}+\frac{{\mathrm{\pi r}}^2}{{\mathrm{\pi r}}^2\mathrm{h}}=\frac{6}{{\mathrm{\pi r}}^2\mathrm{h}} \\ \Rightarrow \frac{1}{\mathrm{r}}+\frac{1}{\mathrm{h}}=6 \end{gathered}$$

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