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:

$D_{1}=28 \ \text{cm} \ \\ D_{2}=44 \ \text{cm} \ \\ \ \\ s=30 \ \text{cm} \ \\ q=1 + \dfrac{ 5 }{ 100 }=\dfrac{ 21 }{ 20 }=1.05 \ \\ \ \\ r_{1}=D_{1}/2=28/2=14 \ \text{cm} \ \\ r_{2}=D_{2}/2=44/2=22 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r_{2}^2 - \pi \cdot \ r_{1}^2=3.1416 \cdot \ 22^2 - 3.1416 \cdot \ 14^2 \doteq 904.7787 \ \text{cm}^2 \ \\ \ \\ S_{2}=\pi \cdot \ r_{1} \cdot \ s=3.1416 \cdot \ 14 \cdot \ 30 \doteq 1319.4689 \ \text{cm}^2 \ \\ \ \\ S=q \cdot \ (S_{1}+S_{2})=1.05 \cdot \ (904.7787+1319.4689) \doteq 2335.46 \doteq 2335 \ \text{cm}^2$

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