Circumference 30781

How many square decimeters of decorative paper are needed to make cone-shaped carnival hats for 46 first-graders if the first-graders head circumference is 49 cm and the cap height is 33 cm? Is it necessary to add 3% paper to the folds?

Correct answer:

X =  393.6187 dm²

Step-by-step explanation:

$$\begin{gathered} n=46 \\ o=49\text{cm} \\ h=33\text{cm} \\ q=100\%+3\%=1+\frac{3}{100}=1.03 \\ o=2\pi r \\ r=o/(2\pi )=49/(2\cdot 3.1416)\doteq 7.7986\text{cm} \\ s=\sqrt{r^2+h^2}=\sqrt{7.7986^2+33^2}\doteq 33.909\text{cm} \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 7.7986\cdot 33.909\doteq 830.7697{\text{cm}}^2 \\ {S}_2=S_1\to {\text{dm}}^2=S_1:100{\text{dm}}^2=830.7697:100{\text{dm}}^2=8.3077{\text{dm}}^2 \\ X=n\cdot q\cdot S_2=46\cdot 1.03\cdot 8.3077=393.6187{\text{dm}}^2 \end{gathered}$$

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