Calculation 81405

Sketch the mesh of a cylinder whose base radius to height ratio is 2 : 3. Calculate the volume and surface of the cylinder if its height is 9 cm (sketch, calculation, answer).

Correct answer:

V =  1017.876 cm³
S =  565.4867 cm²

Step-by-step explanation:

$$\begin{gathered} h=9\text{cm} \\ r:h=2:3 \\ r=\frac{2}{3}\cdot h=\frac{2}{3}\cdot 9=\frac{2\cdot 9}{3}=\frac{18}{3}=6\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 6^2\doteq 113.0973{\text{cm}}^2 \\ V=S_1\cdot h=113.0973\cdot 9=1017.876{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} S_2=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 6\cdot 9\doteq 339.292{\text{cm}}^2 \\ S=2\cdot S_1+S_2=2\cdot 113.0973+339.292=565.4867{\text{cm}}^2 \end{gathered}$$

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