Round skirt

The cut on the round skirt has the shape of an annulus. Determine how much m² of fabric will be consumed on an 80 cm long skirt. The waist circumference is a circle with a smaller radius of 69 cm.

Final Answer:

S =  2.5626 m²

Step-by-step explanation:

$$\begin{gathered} o_1=69\text{cm}\to \text{m}=69:100\text{m}=0.69\text{m} \\ {r}_1=o_1/(2\pi )=0.69/(2\cdot 3.1416)\doteq 0.1098\text{m} \\ x=80\text{cm}\to \text{m}=80:100\text{m}=0.8\text{m} \\ {r}_2=r_1+x=0.1098+0.8\doteq 0.9098\text{m} \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 0.1098^2\doteq 0.0379{\text{m}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 0.9098^2\doteq 2.6005{\text{m}}^2 \\ S=S_2-S_1=2.6005-0.0379=2.5626{\text{m}}^2 \end{gathered}$$

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