Cylinder - area

The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of the cylinder if its volume is 2 m³.

Final Answer:

S =  9.8574 m²

Step-by-step explanation:

$$\begin{gathered} V=2{\text{m}}^3 \\ V=\pi r^{2}h \\ D=2r=h/3 \\ h=6r \\ V=6\pi r^3 \\ r=\sqrt[ \\ 3]{\frac{V}{6\pi }}=\sqrt[ \\ 3]{\frac{2}{6\cdot 3.1416}}\doteq 0.4734\text{m} \\ h=6\cdot r=6\cdot 0.4734\doteq 2.8405\text{m} \\ S=2\pi \cdot r^2+2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 0.4734^2+2\cdot 3.1416\cdot 0.4734\cdot 2.8405=9.8574{\text{m}}^2 \end{gathered}$$

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