A Pile of salt

A Pile of salt has been stored in the shape of a cone. Mr. Terwilliker knows that the pile is 20 feet tall and 102 feet in circumference at the base. What area of the conical tarpaulin (a large sheet of material) is needed to cover the pile?

Correct answer:

S =  1313.7192 ft²

Step-by-step explanation:

$$\begin{gathered} h=20\text{ft} \\ o=102\text{ft} \\ o=2\cdot \pi \cdot r \\ r=\frac{o}{2\pi }=\frac{102}{2\cdot 3.1416}\doteq 16.2338 \\ {s}^2=h^2+r^2 \\ s=\sqrt{h^2+r^2}=\sqrt{20^2+16.2338^2}\doteq 25.7592\text{ft} \\ S=\pi \cdot r\cdot s=3.1416\cdot 16.2338\cdot 25.7592=1313.7192{\text{ft}}^2 \end{gathered}$$

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