Surface of the cylinder

Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.

Correct answer:

S =  70.0527 dm²

Step-by-step explanation:

$$\begin{gathered} V=45l=\pi r^{2}h \\ 2\pi r=3h \\ h={\displaystyle \frac{2}{3}}\pi r \\ V={\displaystyle \frac{2}{3}}{\pi }^2{r}^3 \\ r=\sqrt[3]{{\displaystyle \frac{3V}{2{\pi }^2}}}=1.9dm \\ h={\displaystyle \frac{2}{3}}\pi r=3.98dm \\ S=2\pi r^2+2\pi rh=2\pi \cdot 1.9^2+2\pi \cdot 1.9\cdot 3.98=70.0527{\text{dm}}^2 \end{gathered}$$

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