Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.

Result

S =  2335 cm2

#### Solution:

$D_{1}=28 \ \text{cm} \ \\ D_{2}=44 \ \text{cm} \ \\ \ \\ s=30 \ \text{cm} \ \\ q=1 + \dfrac{ 5 }{ 100 }=\dfrac{ 21 }{ 20 }=1.05 \ \\ \ \\ r_{1}=D_{1}/2=28/2=14 \ \text{cm} \ \\ r_{2}=D_{2}/2=44/2=22 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r_{2}^2 - \pi \cdot \ r_{1}^2=3.1416 \cdot \ 22^2 - 3.1416 \cdot \ 14^2 \doteq 904.7787 \ \text{cm}^2 \ \\ \ \\ S_{2}=\pi \cdot \ r_{1} \cdot \ s=3.1416 \cdot \ 14 \cdot \ 30 \doteq 1319.4689 \ \text{cm}^2 \ \\ \ \\ S=q \cdot \ (S_{1}+S_{2})=1.05 \cdot \ (904.7787+1319.4689) \doteq 2335.46 \doteq 2335 \ \text{cm}^2$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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