Carpet area

The carpet is wound on a cardboard roll in the shape of a cylinder with a diameter of d=12 cm and a length of l=2 m. The rolled-up carpet has an outer diameter of D=38 cm, and the thickness of the rug is 8 mm. What area can the carpet cover after unfolding? Do not consider the deformation caused by winding the carpet on the roll. Result in tenths of m².

Final Answer:

S =  25.53 m²

Step-by-step explanation:

$$\begin{gathered} D_1=12\text{cm}\to \text{m}=12:100\text{m}=0.12\text{m} \\ {D}_2=38\text{cm}\to \text{m}=38:100\text{m}=0.38\text{m} \\ l=2\text{m} \\ h=8\text{mm}\to \text{m}=8:1000\text{m}=0.008\text{m} \\ {r}_1=D_1/2=0.12/2=\frac{3}{50}=0.06\text{m} \\ {r}_2=D_2/2=0.38/2=\frac{19}{100}=0.19\text{m} \\ {S}_1=\pi \cdot r_2^2-\pi \cdot r_1^2=3.1416\cdot 0.19^2-3.1416\cdot 0.06^2\doteq 0.1021{\text{m}}^2 \\ x=S_1/h=0.1021/0.008\doteq 12.7627\text{m} \\ S=l\cdot x=2\cdot 12.7627=25.53{\text{m}}^2 \end{gathered}$$

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