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?

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≐934.4918=934.492 cm2D = 30 \ cm \ \\ v = 10 \ cm \ \\ \ \\ r = D/2 = 30/2 = 15 \ cm \ \\ q = 1 + \dfrac{ 10 }{ 100 } = \dfrac{ 11 }{ 10 } = 1.1 \ \\ \ \\ s = \sqrt{ v^2 + r^2 } = \sqrt{ 10^2 + 15^2 } = 5 \ \sqrt{ 13 } \ cm \doteq 18.0278 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r \cdot \ s = 3.1416 \cdot \ 15 \cdot \ 18.0278 \doteq 849.538 \ cm^2 \ \\ S = q \cdot \ S_{ 1 } = 1.1 \cdot \ 849.538 \doteq 934.4918 = 934.492 \ cm^2

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