Circular dragon

The dragon has the shape of a circular section with a central angle of 40° and a radius of 35 cm. How much paper do we need to make if 10% is added to the curved ones?

Final Answer:

S =  470.3662 cm²

Step-by-step explanation:

$$\begin{gathered} \alpha =40{}^{\circ } \\ r=35\text{cm} \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ {S}_1=\pi \cdot r^2=3.1416\cdot 35^2\doteq 3848.451{\text{cm}}^2 \\ k=\frac{\alpha }{360}=\frac{40}{360}=\frac{1}{9}\doteq 0.1111 \\ S=q\cdot k\cdot S_1=1.1\cdot 0.1111\cdot 3848.451=470.3662{\text{cm}}^2 \end{gathered}$$

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