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 answer:

S =  934.4918 cm²

Step-by-step explanation:

$$\begin{gathered} D=30\text{ cm } \\ v=10\text{ cm } \\ r=D\mathrm{/}2=30\mathrm{/}2=15\text{ cm } \\ q=1+{\displaystyle \frac{10}{100}}={\displaystyle \frac{11}{10}}=1.1 \\ s=\sqrt{v^2+r^2}=\sqrt{10^2+15^2}=5\sqrt{13}\text{ cm}\doteq 18.0278\text{ cm } \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 15\cdot 18.0278\doteq 849.538{\text{cm}}^2 \\ S=q\cdot S_1=1.1\cdot 849.538=934.4918{\text{cm}}^2 \end{gathered}$$

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