Lampshade

The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm2 of material will we need when we 10% is waste?

Correct result:

S =  934.492 cm2

Solution:

D=30 cm v=10 cm  r=D/2=30/2=15 cm q=1+10100=1110=1.1  s=v2+r2=102+152≐5 13 cm≐18.0278 cm  S1=π⋅ r⋅ s=3.1416⋅ 15⋅ 18.0278≐849.538 cm2 S=q⋅ S1=1.1⋅ 849.538=934.492 cm2D=30 \ \text{cm} \ \\ v=10 \ \text{cm} \ \\ \ \\ r=D/2=30/2=15 \ \text{cm} \ \\ q=1 + \dfrac{ 10 }{ 100 }=\dfrac{ 11 }{ 10 }=1.1 \ \\ \ \\ s=\sqrt{ v^2 + r^2 }=\sqrt{ 10^2 + 15^2 } \doteq 5 \ \sqrt{ 13 } \ \text{cm} \doteq 18.0278 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 15 \cdot \ 18.0278 \doteq 849.538 \ \text{cm}^2 \ \\ S=q \cdot \ S_{1}=1.1 \cdot \ 849.538=934.492 \ \text{cm}^2

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