Deformation 6260

The carpet is wound on a cardboard roll in the shape of a cylinder with a diameter of d=12cm and a length of l=2m. The rolled-up carpet has an outer diameter of D=38cm, and the thickness of the rug is 8mm. 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.

Correct 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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