Rotary cylinder 2

The base circumference of the rotary cylinder has the same length as its height. What is the surface area of the cylinder if its volume is 250 dm³?

Correct answer:

S =  248.64 dm²

Step-by-step explanation:

$$\begin{gathered} V=250{\text{dm}}^3 \\ h=2\pi r \\ V=\pi r^{2}h=\pi r^2\cdot 2\pi r=2\cdot {\pi }^2{r}^3 \\ r=\sqrt[3]{\frac{V}{2{\pi }^2}}=\sqrt[3]{\frac{250}{2\cdot 3.1416^2}}\doteq 2.331\text{dm} \\ h=2\pi \cdot r=2\cdot 3.1416\cdot 2.331\doteq 14.6459\text{dm} \\ S=2\pi \cdot r^2+2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 2.331^2+2\cdot 3.1416\cdot 2.331\cdot 14.6459=248.64{\text{dm}}^2 \end{gathered}$$

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