The collar

The collar on the dress has the shape of an annulus 6 cm wide. The circumference of the inner circle is 31.4 cm. How much cm² of fabric is needed to make one collar?

Correct answer:

S =  301.4973 cm²

Step-by-step explanation:

$$\begin{gathered} h=6\text{ cm } \\ {o}_2=31.4\text{ cm } \\ {r}_2=o_2\mathrm{/}(2\pi )=31.4\mathrm{/}(2\cdot 3.1416)\doteq 4.9975\text{ cm } \\ {r}_1=r_2+h=4.9975+6\doteq 10.9975\text{ cm } \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 10.9975^2\doteq 379.9575{\text{cm}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 4.9975^2\doteq 78.4602{\text{cm}}^2 \\ S=S_1-S_2=379.9575-78.4602=301.4973{\text{cm}}^2 \end{gathered}$$

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