From the figure sketched above:
l= slant height=16in
diameter=13in, so we need to get the radius
r=radius=diameter/2
[tex]r=\frac{13}{2}=6.5in[/tex]The figure above is a Cone.
[tex]\text{Volume of the cone=}\frac{1}{3}\pi\times r^2\sqrt[]{l^2-r^2}[/tex][tex]\begin{gathered} V=\frac{1}{3}\times3.14\times6.5^2\sqrt[]{16^2-6.5^2} \\ V=\frac{1}{3}\times3.14\times42.25\sqrt[]{256-42.25} \\ V=\frac{1}{3}\times3.14\times42.25\times\sqrt[]{213.75} \end{gathered}[/tex][tex]\begin{gathered} V=\frac{1}{3}\times3.14\times42.25\times14.62 \\ V=\frac{1939.5623}{3}=646.5208\approx646.52in^3 \end{gathered}[/tex]Hence, the volume of the cone is 646.52in³.
