Shell area cy

The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.

Correct result:

V =  596.831 cm³

Solution:

$$\begin{gathered} S=300{\text{cm}}^2 \\ h=12\text{ cm } \\ S=2\pi \cdot r\cdot h \\ r={\displaystyle \frac{S}{2\pi \cdot h}}={\displaystyle \frac{300}{2\cdot 3.1416\cdot 12}}\doteq 3.9789\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3.9789^2\doteq 49.7359{\text{cm}}^2 \\ V=S_1\cdot h=49.7359\cdot 12=596.831{\text{cm}}^3 \end{gathered}$$

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