The cap

A jester's hat is in the shape of a cone. Calculate how much paper is needed to make a hat 53 cm tall for a head circumference of 45 cm.

Final Answer:

S =  1203.3386 cm²

Step-by-step explanation:

$$\begin{gathered} v=53\text{cm} \\ o=45\text{cm} \\ o=2\pi r \\ r=\frac{o}{2\pi }=\frac{45}{2\cdot 3.1416}\doteq 7.162\text{cm} \\ s=\sqrt{r^2+v^2}=\sqrt{7.162^2+53^2}\doteq 53.4817\text{cm} \\ S=\pi \cdot r\cdot s=3.1416\cdot 7.162\cdot 53.4817=1203.3386{\text{cm}}^2 \end{gathered}$$

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