Respuesta :

[tex]\bf \textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=11 \end{cases}\implies LA=\pi (5)\sqrt{5^2+11^2} \\\\\\ LA=5\pi \sqrt{146}\implies LA\approx 189.8[/tex]

Answer:

Lateral Surface area of cone is 190 unit².

Step-by-step explanation:

Given: Height of cone , h = 11 unit

           Radius of cone , r = 5 unit

To find: Lateral Surface Area

Slant height , l = [tex]\sqrt{r^2+h^2}[/tex]

[tex]l=\sqrt{5^2+11^2}[/tex]

[tex]l=\sqrt{25+121}[/tex]

[tex]l=\sqrt{146}[/tex]

Lateral surface area = [tex]\pi rl[/tex]

                                 = [tex]\frac{22}{7}\times5\times\sqrt{146}[/tex]

                                 = [tex]189.876436728[/tex]

                                 = [tex]190\:unit^2\:(approx.)[/tex]

Therefore, Lateral Surface area of cone is 190 unit².

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