Twenty percent

The students in the class agreed to make various decorative cone-shaped hats for the carnival. How much decorative material did a class of 25 students need to make the hats, if they had to allow for approximately twenty percent waste when cutting and gluing? (The dimensions of the hats are: base radius 7.5 cm, height 25 cm.)

Final Answer:

S =  1.845 m²

Step-by-step explanation:

$$\begin{gathered} n=25 \\ r=7.5\text{cm} \\ h=25\text{cm} \\ s=\sqrt{r^2+h^2}=\sqrt{7.5^2+25^2}\doteq 26.1008\text{cm} \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 7.5\cdot 26.1008\doteq 614.9848{\text{cm}}^2 \\ {S}_2=S_1\to {\text{m}}^2=S_1:10000{\text{m}}^2=614.9848:10000{\text{m}}^2=0.0615{\text{m}}^2 \\ q=100\%+20\%=1+\frac{20}{100}=1.2 \\ S=n\cdot q\cdot S_2=25\cdot 1.2\cdot 0.0615=1.845{\text{m}}^2 \end{gathered}$$

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