Diameter 132

The base diameter of a rotating cylinder is 2 m and its surface area is 34.54 m². Calculate the base radius of the given rotating cylinder, its height and volume.

Final Answer:

r =  1 m
h =  4.4972 m
V =  14.1284 m³

Step-by-step explanation:

$$\begin{gathered} D=2\text{m} \\ S=34.54{\text{m}}^2 \\ r=D/2=2/2=1\text{m} \end{gathered}$$

$$\begin{gathered} S_1=\pi \cdot r^2=3.1416\cdot 1^2\doteq 3.1416{\text{m}}^2 \\ S=2\cdot S_1+S_2 \\ {S}_2=S-2\cdot S_1=34.54-2\cdot 3.1416\doteq 28.2568{\text{m}}^2 \\ {S}_2=\pi \cdot D\cdot h \\ h=\frac{S_2}{\pi \cdot D}=\frac{28.2568}{3.1416\cdot 2}=4.4972\text{m} \end{gathered}$$

$V=S_1\cdot h=3.1416\cdot 4.4972=14.1284{\text{m}}^3$

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