Question

A cone-shaped lampshade has a height of 18 cm and a slant height of 19.5 cm. Find the lateral surface area of the lampshade.

Answer 1

Check the picture below.

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2-b^2)=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ √(19.5^2-18^2)=r\implies √(56.25)=r \\\\[-0.35em] ~\dotfill`

`\textit{lateral area of a cone}\\\\ LA=\pi r√(r^2+h^2)~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{√(r^2+h^2)}\\[-0.5em] \hrulefill\\ r=√(56.25) \end{cases}\implies \begin{array}{llll} LA=\pi √(56.25)\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}`