Surface of the cylinder

Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm

Result

S =  25.197 cm2

Solution:

S1=20 cm2 v=3.5 cm  S1=2 πrv  r=S1/(2π⋅ v)=20/(2⋅ 3.1416⋅ 3.5)≐0.9095 cm  S2=π⋅ r2=3.1416⋅ 0.90952≐2.5984 cm2  S=S1+2⋅ S2=20+2⋅ 2.5984≐25.1969≐25.197 cm2S_{1}=20 \ \text{cm}^2 \ \\ v=3.5 \ \text{cm} \ \\ \ \\ S_{1}=2 \ \pi r v \ \\ \ \\ r=S_{1} / (2 \pi \cdot \ v)=20 / (2 \cdot \ 3.1416 \cdot \ 3.5) \doteq 0.9095 \ \text{cm} \ \\ \ \\ S_{2}=\pi \cdot \ r^2=3.1416 \cdot \ 0.9095^2 \doteq 2.5984 \ \text{cm}^2 \ \\ \ \\ S=S_{1} + 2 \cdot \ S_{2}=20 + 2 \cdot \ 2.5984 \doteq 25.1969 \doteq 25.197 \ \text{cm}^2

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