Insulation

A special rubber pipe insulator is used to insulate the supply pipes of solar collectors. The product with the description DNa20, thickness 25 mm, 2 m corresponds to insulation for pipes with a diameter of 20 mm and a rubber layer thickness of 25 mm, sold in two-metre pieces. Determine the volume of one piece of rubber insulation in dm³.

Final Answer:

V =  7068.5835 cm³

Step-by-step explanation:

$$\begin{gathered} h=25\text{mm}\to \text{cm}=25:10\text{cm}=2.5\text{cm} \\ l=2\text{m}\to \text{cm}=2\cdot 100\text{cm}=200\text{cm} \\ D=20\text{mm}\to \text{cm}=20:10\text{cm}=2\text{cm} \\ {r}_1=D/2=2/2=1\text{cm} \\ {r}_2=r_1+h=1+2.5=\frac{7}{2}=3.5\text{cm} \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 1^2\doteq 3.1416{\text{cm}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 3.5^2\doteq 38.4845{\text{cm}}^2 \\ S=S_2-S_1=38.4845-3.1416\doteq 35.3429{\text{cm}}^2 \\ V=S\cdot l=35.3429\cdot 200=7068.5835{\text{cm}}^3 \end{gathered}$$

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