Lampshade 3

A lampshade has the shape of a lateral surface of a cone with a slant height of 32 cm and a base diameter of 46 cm.
Calculate the paper needed for its production, assuming 6% waste.

Final Answer:

S =  24.51 dm²

Step-by-step explanation:

$$\begin{gathered} s=32\text{cm}\to \text{dm}=32:10\text{dm}=3.2\text{dm} \\ D=46\text{cm}\to \text{dm}=46:10\text{dm}=4.6\text{dm} \\ r=D/2=4.6/2=\frac{23}{10}=2.3\text{dm} \\ q=100\%+6\%=1+\frac{6}{100}=1.06 \\ {s}^2=v^2+r^2 \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 2.3\cdot 3.2\doteq 23.1221{\text{dm}}^2 \\ S=q\cdot S_1=1.06\cdot 23.1221=24.51{\text{dm}}^2 \end{gathered}$$

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