1. We can find lateral area of a cone by [tex]\text{Lateral area}=\pi*r*l[/tex], where r equals radius of cone and l equals slant height of cone.
We can find slant height of our cone using Pythagorean theorem.
[tex]l=\sqrt{11^{2}+5^{2}}[/tex]
[tex]l=\sqrt{121+25}[/tex]
[tex]l=\sqrt{146}[/tex]
Let us substitute our slant height in lateral area formula.
[tex]\text{Lateral area}=\pi*5\sqrt{146}[/tex]
Therefore, our lateral area will be [tex]\pi*5\sqrt{146}[/tex] square units.
2. [tex]\text{Volume of cone}=\frac{1}{3} \cdot\pi\cdot r^{2}\cdot h[/tex]
Upon substituting our given values in volume formula we will get,
[tex]\text{Volume of cone}=\frac{1}{3} \cdot\pi\cdot 5^{2}\cdot 11[/tex]
[tex]\text{Volume of cone}=\frac{1}{3} \cdot\pi \cdot 25\cdot 11[/tex]
[tex]\text{Volume of cone}=\frac{275}{3} \cdot\pi[/tex]
[tex]\text{Volume of cone}=91\frac{2}{3} \cdot\pi[/tex]
Therefore, volume of our cone will be [tex]91\frac{2}{3} \cdot\pi[/tex] cubic units.
