# 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:

$h=70 \ \text{cm} \ \\ D_{1}=180 \ \text{cm} \ \\ D_{2}=120 \ \text{cm} \ \\ \ \\ o_{1}=\pi \cdot \ D_{1}=3.1416 \cdot \ 180 \doteq 565.4867 \ \text{cm} \ \\ o_{2}=\pi \cdot \ D_{2}=3.1416 \cdot \ 120 \doteq 376.9911 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ (D_{1}/2)^2=3.1416 \cdot \ (180/2)^2 \doteq 25446.9005 \ \text{cm}^2 \ \\ S_{2}=\pi \cdot \ (D_{2}/2)^2=3.1416 \cdot \ (120/2)^2 \doteq 11309.7336 \ \text{cm}^2 \ \\ \ \\ M=2 \cdot \ (S_{1}-S_{2})=2 \cdot \ (25446.9005-11309.7336) \doteq 28274.3339 \ \text{cm}^2 \ \\ \ \\ S=M + o_{1} \cdot \ h+o_{2} \cdot \ h=28274.3339 + 565.4867 \cdot \ 70+376.9911 \cdot \ 70=94247.78 \ \text{cm}^2$

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