Cone shelter shell

A cone-shaped shelter with a base diameter of 4 m was built on a children's playground. Calculate the lateral surface area of the cone if the slant height is 8 m.

Final Answer:

S =  50.2655 m²

Step-by-step explanation:

$$\begin{gathered} D=4\text{m} \\ s=8\text{m} \\ r=D/2=4/2=2\text{m} \\ {s}^2=h^2+r^2 \\ h=\sqrt{s^2-r^2}=\sqrt{8^2-2^2}=2\sqrt{15}\text{m}\doteq 7.746\text{m} \\ S=\pi \cdot r\cdot s=3.1416\cdot 2\cdot 8=50.2655{\text{m}}^2 \end{gathered}$$

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