Find the following measures for this figure. Lateral Area = 55 square units 5√(47) square units 5√(146) square units Volume = 275 cubic units 91 2/3 cubic units 36 2/3 cubic units

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.