The hollow cylinder

The hollow cylinder has a height of 70 cm, an outer diameter of 180 cm and an inner diameter of 120 cm. What is the surface of the body, including the area inside the cavity?

Correct result:

S =  94247.78 cm2

Solution:

h=70 cm D1=180 cm D2=120 cm  o1=π D1=3.1416 180565.4867 cm o2=π D2=3.1416 120376.9911 cm  S1=π (D1/2)2=3.1416 (180/2)225446.9005 cm2 S2=π (D2/2)2=3.1416 (120/2)211309.7336 cm2  M=2 (S1S2)=2 (25446.900511309.7336)28274.3339 cm2  S=M+o1 h+o2 h=28274.3339+565.4867 70+376.9911 70=94247.78 cm2h=70 \ \text{cm} \ \\ D_{1}=180 \ \text{cm} \ \\ D_{2}=120 \ \text{cm} \ \\ \ \\ o_{1}=\pi \cdot \ D_{1}=3.1416 \cdot \ 180 \doteq 565.4867 \ \text{cm} \ \\ o_{2}=\pi \cdot \ D_{2}=3.1416 \cdot \ 120 \doteq 376.9911 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ (D_{1}/2)^2=3.1416 \cdot \ (180/2)^2 \doteq 25446.9005 \ \text{cm}^2 \ \\ S_{2}=\pi \cdot \ (D_{2}/2)^2=3.1416 \cdot \ (120/2)^2 \doteq 11309.7336 \ \text{cm}^2 \ \\ \ \\ M=2 \cdot \ (S_{1}-S_{2})=2 \cdot \ (25446.9005-11309.7336) \doteq 28274.3339 \ \text{cm}^2 \ \\ \ \\ S=M + o_{1} \cdot \ h+o_{2} \cdot \ h=28274.3339 + 565.4867 \cdot \ 70+376.9911 \cdot \ 70=94247.78 \ \text{cm}^2



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