Barrel-shaped 40601

The barrel-shaped cylinder has a volume of 9.42 hl, and the inner diameter of the bottom is 12 dm. Calculate the area of the barrel shell in m². Solve in general first.

Final Answer:

S =  3.14 m²

Step-by-step explanation:

$$\begin{gathered} V=9.42\text{hl}\to {\text{m}}^3=9.42:10{\text{m}}^3=0.942{\text{m}}^3 \\ D=12\text{dm}\to \text{m}=12:10\text{m}=1.2\text{m} \\ r=D/2=1.2/2=\frac{3}{5}=0.6\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 0.6^2\doteq 1.131{\text{m}}^2 \\ V=S_1\cdot h \\ h=V/S_1=0.942/1.131\doteq 0.8329\text{m} \\ S=\pi \cdot D\cdot h=3.1416\cdot 1.2\cdot 0.8329=3.14{\text{m}}^2 \end{gathered}$$

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